Cyclotomic Polynomials at x=n, n! and sigma(n)

There are many sequences in the OEIS dealing with cyclotomic polynomials, factorials and the divisor function, sigma.

Selected sequences and those related to prime terms are summarized here.

A000203 a(n)=sigma(n): lists many references and links.

The table below summarizes sequences in the OEIS related to prime terms of the cyclotomic polynomials,$\Phi _{k}(X)$ with $X=n,n!and\sigma (n)$.

Related Sequences

Column headings in the table below:

k                  Cyclotomic index
$\Phi _{k}(X)$                Polynomial: $\Phi _{k}(X)$

$\Phi _{k}(n)$                A-number of sequence listing values where $x=n$
Indices $\Phi _{k}(n)$        A-number of sequence listing indices of primes where $x=n$
Primes $\Phi _{k}(n)$         A-number of sequence listing primes where $x=n$

$\Phi _{k}(n!)$               A-number of sequence listing values where $x=n!$
Indices $\Phi _{k}(n!)$       A-number of sequence listing indices of primes where $x=n!$
Primes $\Phi _{k}(n!)$        A-number of sequence listing primes where $x=n!$

$\Phi _{k}(\sigma (n))$              A-number of sequence listing values where $x=\sigma (n)$
Indices $\Phi _{k}(\sigma (n))$      A-number of sequence listing indices of primes where $x=\sigma (n)$
Primes $\Phi _{k}(\sigma (n))$       A-number of sequence listing primes where $x=\sigma (n)$

Sequences

k				Indices	Primes			Indices	Primes			Indices	Primes
1			A023443	A008864	A000040		A033312	A002982	A055490		A039653	A248792	A248793
2			A000027	A006093	A000040		A038507	A002981	A088332		A088580	A065512	A258430
3			A002061(n+1)	A002384	A002383		A066142	A051856	A162455		A258774	A258775	A258776
4			A002522	A005574	A002496		A020549	A046029	A051739		A258974	A258976	A258977
5			A053699	A049409	A088548		A259264	A200906	A259265		A258978	A258979	A258980
6			A002061	A055494	A002383			A051857			A259184	A259185	A259186
7			A053716	A100330	A088550			A258357			A259251	A259252	A259253
8			A123865	A000068	A037896						A259308	A259309	A259310
9			A060883	A153439	A162601			A258355			A259369	A259370	A259371
10			A060884	A246392	A259257			A258356			A259410	A259411	A259412