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

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

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

Programs

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));

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.