Divisors:

A000005: Divisor counting function (

*σ*_0(

*n*),

*τ*(n),

*d*(

*n*)).

A027750: Divisors of

*n*.

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*).

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.

Nondivisors:

A049820: Nondivisor counting function.

A173540: Nondivisors of

*n*.

Nondivisors in the cototient (numbers 1 <

*m*<

*n*"neutral" to

*n*):

A045763: Neutral counting function.

A133995: Neutrals of

*n*.

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.

A162306: regulars of

*n*.

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*.*

A293555: A243822 recordsetters.*

A293556: Records in A243822.*

Semitotatives (nonregulars in the cototient of

*n*):

A243823: Semitotative counting function.*

A272619: Semitotatives of

*n*.*

A292867: A243823 recordsetters.*

A293868: Records in A243823.*

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.*

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).*

"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.**

* sequences I'd added based on research presented here.

** current drafts.