A341523 Number of prime factors (with multiplicity) shared by n and sigma(n): a(n) = bigomega(gcd(n, sigma(n))).

0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 0, 0, 1, 1, 0, 2, 0, 3, 0, 1, 0, 3, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 1, 2, 0, 3, 1, 2, 0, 1, 1, 3, 0, 0, 1, 0, 0, 2, 0, 1, 1

Offset: 1

Author

Antti Karttunen, Feb 17 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A009194, A014567 (positions of zeros), A341519, A341524.

Programs

Mathematica

Table[PrimeOmega[GCD[n, DivisorSigma[1, n]]], {n, 1, 100}] (* Amiram Eldar, Feb 17 2021 *)

PARI

A341523(n) = bigomega(gcd(n, sigma(n)));

Formula

a(n) = A001222(A009194(n)).

a(n) = A001222(n) - A341524(n).

a(A003961(n)) = A341519(n).