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

2,11

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) = 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).

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

Crossrefs

Cf. A000430 (positions of 0's), A000523, A001222, A003961, A061395, A070939, A156552, A246277, A322993, A325134, A339893, A342655, A342656.

Cf. also A339895.

Sequence in context: A353496 A170942 A325660 * A002187 A124756 A113504

Adjacent sequences: A342654 A342655 A342656 * A342658 A342659 A342660

Keyword

nonn

Author

Antti Karttunen, Mar 18 2021

Status

approved