OEIS Sources

Check out the map of all "digits" of "bases" less than 2310. Boxes ■ attempt to key the relationships to this map.

Divisors:
A000005: Divisor counting function (σ0(n), τ(n), d(n)).
A027750: Divisors of n.
A051731: Characteristic function of the divisors: 1 if m | n, 0 if not (useful in producing maps).
                 ■ These show on the map as red pixels. The first pixel is always purple ■, as 1 is also a totative.
A002182: A000005 recordsetters. (Highly composite numbers).
A002183: Records in A000005.

Totatives:
A000010: Euler totient function (Totative counting function) (φ(n)).
A038566: Totatives of n (reduced residue system of n).
A054521: Characteristic function of the totatives: 1 if gcd(m, n) = 1, 0 if not.
                 ■ These show on the map as light gray pixels. The first pixel is always purple ■, as 1 is also a divisor.
A000040: A000010 recordsetters (the primes).
A006093: Records in A000010 (primes p - 1).

Cototient: (non-totatives):
A051953: Cototient counting function.
A121998: Numbers m < n in the cototient of n.
A065385: A051953 recordsetters.
A065386: Records in A051953.
                 ■■■ These show on the map as red, orange, or yellow pixels.

Nondivisors:
A049820: Nondivisor counting function.
A173540: Nondivisors of n.
                 ■■■ These show on the map as orange, yellow, or light gray pixels.

Nondivisors in the cototient (numbers 1 < m < n "neutral" to n):
A045763: Neutral counting function.
A133995: Neutrals of n.
A304571: Characteristic function of nondivisors in the cototient of n.*
                 ■■ These show on the map as orange or yellow pixels.
A300859: A045763 recordsetters (highly neutral numbers)*
A300914: Records in A045763.*

Regulars (here, numbers 1 < m < n such that m divides n^e with e ≥ 0):
A010846: Regular counting function. ( rcf(n). We can calculate regulars m < lim for lim > n with rcf(n, lim) )
A162306: regulars of n.
A304569: Characteristic function of numbers m such that m | n^e with e ≥ 0.*
                 ■■■ These show on the map as purple, red, or orange pixels.
A244052: A010846 recordsetters (Highly regular numbers).*
A244053: Records in A010846.*

Semidivisors (numbers 1 < m < n such that m divides n^e with e > 1):
A243822: Semidivisor counting function.*
A272618: Semidivisors of n.*
A304570: Characteristic function of numbers m such that m | n^e with e > 1.*
                 ■ These show on the map as orange pixels.
A293555: A243822 recordsetters.*
A293556: Records in A243822.*
A289280: Smallest semidivisor m > n.

Semitotatives (nonregulars in the cototient of n):
A243823: Semitotative counting function.*
A272619: Semitotatives of n.*
A304572: Characteristic function of numbers m such that m divides no integer power of n yet gcd(m, n) > 1.*
                 ■ These show on the map as yellow pixels.
A292867: A243823 recordsetters.*
A293868: Records in A243823.*
A096014: Smallest m semicoprime to n: product of least prime factor p and smallest prime q that does not divide n.
A291989: Least m > n semicoprime to n.*

Richness of regulars of n: (richness meaning the least power n^e that regular m divides):
A279907: Richness of numbers in the range n.*
A280269: Richness of row n of A162306.*
A280274: Maximum richness in row n of A162306.*
A280363: Underlying formula for A280274.*
A294306: Population of values in row n of A280269.*
A316991: Richness of A289280(n) (the smallest semidivisor that exceeds n).**

Study of "Highly Regular Numbers" A244052 (2016-7 "Turbulent Candidates" paper):
A288784: Necessary but insufficient condition.*
A288813: Turbulent candidates in A288784.*
A289171: "Depth"-"Distension" correlation for primorial(n).*
A3xxxxx: rcf(A002110(i), m) - A010846(m) for m in A288813 (Deficit of rcf(m) versus rcf(n, m)).

"Dominance" studies:
A294575: Semitotative-dominant numbers.*
A294576: Odd Semitotative-dominant numbers.*
A295221: Semitotative parity numbers.*
A295523: Nonprimes that have more semidivisors than semitotatives.*
A294492: Recordsetters for A045763(n)/n.*

Semidivisors vs. Divisors:
A299990: A243822(n) - A000005(n).*
A299991: Numbers that have more semidivisors than divisors.*
A299992: Numbers with more than 1 distinct prime divisor that have fewer semidivisors than divisors.*
A300155: Numbers that have equal numbers of semidivisors and divisors.*
A300156: A299990 recordsetters.*
A300157: Records in A299990.*

Semitotatives vs. Semidivisors:
A300858: A243823(n) - A243822(n). (A300858(p) for p prime = 0, for n = {6, 10, 12, 18, 30}, A300858(n) is negative.)
A300860: A300858 recordsetters.*
A300861: Records in A300858.*

Numbers m highly composite or superabundant, plotted as (x, y) = (m/p_ω(m)#, ω(m)).
A108602: ω(m)# for highly composite m.
A305025: ω(m)# for superabundant m.
A301413: m/p_ω(m)# for highly composite m.
A305056: m/p_ω(m)# for superabundant m.
A301416: m/p_ω(m)# for superior highly composite m.
A3xxxxx: m/p_ω(m)# for colossally abundant m.
A301414: Primitive values in A301413.
A3xxxxx: Primitive values of m/p_ω(m)# for superabundant m.
A3xxxxx: Primitive values of m/p_ω(m)# for superior highly composite m.
A3xxxxx: Primitive values of m/p_ω(m)# for colossally abundant m.
A301415: Number of primorials such that A301414(n) produces highly composite m.
A3xxxxx: Number of primorials such that primitive values of m/p_ω(m)# produces superabundant m.
A3xxxxx: Smallest k such that p_k# × A301414(n) produces highly composite m.
A3xxxxx: Largest k such that p_k# × A301414(n)  produces highly composite m.
A3xxxxx: Smallest k such that p_k# × primitive values of m/p_ω(m)# produces superabundant m.
A3xxxxx: Largest k such that p_k# × primitive values of m/p_ω(m)# produces superabundant m.

Relating HCNs with products of primorials and primorials themselves.
A306737: Irregular triangle where row n is a list of indices i of pi# with multiplicity whose product is A002182(n).*
A306802: Position of highly composite numbers in the sequence of products of primorials.*
A307056: Row n = digits of A025487(n) in primorial base.*
A307113: Number of highly composite numbers m in the interval pk# ≤ m < p(k+1)#.*
A307133: T(n,m) = number of k ≤ pn# such that Ω(k) = m, where k is a term in A025487.*

* sequences I'd added based on research presented here.
** current drafts.
*** prepared sequences with reserved A-numbers.

Updated 201903261703 CDT.