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

2,9

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

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).

Prog

(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

Crossrefs

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

Cf. also A324117, A324118.

Sequence in context: A239706 A328616 A260736 * A293896 A066416 A292342

Adjacent sequences: A342653 A342654 A342655 * A342657 A342658 A342659

Keyword

nonn

Author

Antti Karttunen, Mar 18 2021

Status

approved