A342655 Number of prime factors (counted with multiplicity) in A156552(n).

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, 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, 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

Offset

2,4

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) = A001222(A156552(n)).

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

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

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

Prog

(PARI)
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};
A342655(n) = bigomega(A156552(n));

Crossrefs

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

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

Sequence in context: A091948 A339443 A369323 * A161901 A102862 A029331

Adjacent sequences: A342652 A342653 A342654 * A342656 A342657 A342658

Keyword

nonn

Author

Antti Karttunen, Mar 18 2021

Status

approved