A341523 - OEIS

%I #9 Feb 17 2021 20:26:35

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A341523/b341523.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(A009194(n)).

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

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

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

%o (PARI) A341523(n) = bigomega(gcd(n, sigma(n)));

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

%K nonn

%O 1,6

%A _Antti Karttunen_, Feb 17 2021