A341524 - OEIS

%I #12 Dec 10 2023 17:23:28

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A341524/b341524.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

%t Table[PrimeOmega[n] - PrimeOmega[GCD[n, DivisorSigma[1, n]]], {n, 1, 100}] (* _Amiram Eldar_, Feb 17 2021 *)

%o (PARI) A341524(n) = (bigomega(n) - bigomega(gcd(n, sigma(n))));

%Y Cf. A001222, A009194, A017666, A341523.

%Y Cf. A007691 (positions of zeros).

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

%K nonn

%O 1,4

%A _Antti Karttunen_, Feb 17 2021