A341524 Number of prime factors in A017666(n), counted with multiplicity: a(n) = bigomega(n) - bigomega(gcd(n, sigma(n))).

0, 1, 1, 2, 1, 0, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 3, 0, 1, 1, 1, 5, 1, 1, 2, 4, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 3, 2, 3, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 3, 6, 2, 1, 1, 2, 1, 2, 1, 4, 1, 1, 3, 1, 2, 1, 1, 4, 4, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 3, 2, 4, 1, 1, 1, 3, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0

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. A001222, A009194, A017666, A341523.

Cf. A007691 (positions of zeros).

Cf. A341608 (applied onto prime shift array A246278).

Programs

Mathematica

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

PARI

A341524(n) = (bigomega(n) - bigomega(gcd(n, sigma(n))));

Formula

a(n) = A001222(A017666(n)).

a(n) = A001222(n) - A341523(n).