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

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

1,11

Links

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

Formula

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

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

Prog

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

Crossrefs

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

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

Sequence in context: A231714 A366445 A354578 * A343606 A112553 A026610

Adjacent sequences: A339890 A339891 A339892 * A339894 A339895 A339896

Keyword

nonn

Author

Antti Karttunen, Dec 21 2020

Status

approved