A342656 a(n) = A087436(A156552(n)); Number of odd prime factors in A156552(n), counted with repetitions.

0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 2, 0, 1, 1, 2, 1, 3, 0, 1, 2, 2, 0, 1, 0, 1, 1, 4, 0, 1, 1, 2, 2, 1, 0, 1, 2, 1, 2, 3, 0, 1, 0, 2, 1, 3, 1, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 2, 0, 1, 2, 2, 0, 3, 2, 3, 4, 4, 0, 3, 2, 2, 3, 4, 2, 2, 0, 2, 2, 2, 0, 3, 0, 1, 2

Offset: 2

Author

Antti Karttunen, Mar 18 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A001222, A003961, A055396, A087436, A156552, A246277, A322993, A342655.

Cf. also A324117, A324118.

Programs

PARI

A087436(n) = (bigomega(n>>valuation(n,2)));
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};
A342656(n) = A087436(A156552(n));

PARI

\\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt
v156552sigs = readvec("a156552.txt");
A342656(n) = if(2==n,0,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); vecsum(es)-((2==ps[1])*es[1])); \\ Antti Karttunen, Jan 29 2022

Formula

a(n) = A087436(A156552(n)) = A001222(A322993(n)).

a(n) = A342655(2*A246277(n)) = 1 + A342655(n) - A055396(n).

a(p) = 0 for all primes p.

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