A342655 - OEIS

%I #14 Jan 29 2022 20:14:50

%S 0,1,1,2,1,3,1,2,2,4,1,5,1,2,2,6,1,7,1,3,2,8,1,3,2,2,2,9,2,10,1,2,2,3,

%T 3,11,1,3,2,12,1,13,1,2,4,14,1,4,2,3,1,15,1,4,1,3,3,16,1,17,2,2,3,3,2,

%U 18,2,2,1,19,2,20,2,2,2,4,2,21,1,3,2,22,3,4,3,5,4,23,3,5,2,4,4,4,2,24,2,3,2,25,3,26,1,3

%N Number of prime factors (counted with multiplicity) in A156552(n).

%H Antti Karttunen, <a href="/A342655/b342655.txt">Table of n, a(n) for n = 2..10000</a> (based on Hans Havermann's factorization of A156552)

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A001222(A156552(n)).

%F a(n) = A342656(n) + A055396(n) - 1.

%F a(A003961(n)) = 1 + a(n).

%F a(A000040(n)) = n-1 for all n >= 1.

%o (PARI)

%o A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};

%o A342655(n) = bigomega(A156552(n));

%Y Cf. A001222, A003961, A055396, A156552, A342656, A342657, A350064.

%Y Cf. also A323243, A324104, A324105, A324119, A342653 (sigma, phi, tau, omega and mu similarly permuted).

%K nonn

%O 2,4

%A _Antti Karttunen_, Mar 18 2021