A342657 -id:A342657 - cp's OEIS frontend

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

Antti Karttunen, Mar 18 2021

nonn

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

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

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

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));

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.

A339893 a(n) = A000523(n) - A001222(n); floor(log_2(n)) minus the number of prime divisors of n, counted with multiplicity.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 3, 1, 3, 1, 2, 2, 3, 0, 2, 2, 1, 1, 3, 1, 3, 0, 3, 3, 3, 1, 4, 3, 3, 1, 4, 2, 4, 2, 2, 3, 4, 0, 3, 2, 3, 2, 4, 1, 3, 1, 3, 3, 4, 1, 4, 3, 2, 0, 4, 3, 5, 3, 4, 3, 5, 1, 5, 4, 3, 3, 4, 3, 5, 1, 2, 4, 5, 2, 4, 4, 4, 2, 5, 2, 4, 3, 4, 4, 4, 0, 5, 3, 3, 2, 5, 3, 5, 2, 3

Offset: 1

Antti Karttunen, Dec 21 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000523, A001222, A029744 (positions of 0's), A339895.

Cf. also A339823, A342657 [= a(A156552(n))].

A339893(n) = (#binary(n) - 1 - bigomega(n));

a(n) = A000523(n) - A001222(n).

a(n) = A339895(A122111(n)).

cp's OEIS Frontend

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

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