A342657 The difference between floor(log_2(.)) of and the number of prime factors in A156552(n) (when counted with multiplicity).

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 1, 1, 0, 2, 0, 3, 1, 3, 0, 3, 0, 4, 1, 3, 0, 2, 0, 3, 3, 5, 1, 1, 0, 7, 3, 3, 0, 4, 0, 5, 2, 5, 0, 4, 0, 2, 4, 6, 0, 3, 1, 5, 5, 7, 0, 4, 0, 9, 3, 2, 3, 4, 0, 6, 7, 4, 0, 3, 0, 10, 2, 7, 1, 5, 0, 5, 1, 11, 0, 3, 3, 11, 5, 3, 0, 2, 1, 8, 7, 11, 4, 4, 0, 3, 3, 3, 0, 5, 0, 7, 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. A000430 (positions of 0's), A000523, A001222, A003961, A061395, A070939, A156552, A246277, A322993, A325134, A339893, A342655, A342656.

Cf. also A339895.

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};
A342657(n) = { my(u=A156552(n)); (#binary(u)-bigomega(u))-1; };

Formula

a(n) = A339893(A156552(n)) = A339893(A322993(n)) = A000523(A156552(n)) - A001222(A156552(n)).

a(n) = (A252464(n)-A342655(n))-1 = (A325134(n)-A342655(n)) - 2.

a(p) = a(p^2) = 0 for all primes p. (Second part added Jul 27 2023)

a(A003961(n)) = a(2*A246277(n)) = a(n).