A324735 Difference between the binary length and the binary weight of A324712. a(n) = 0 if A324712(n) = 0.

0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 2, 2, 0, 3, 1, 3, 3, 2, 0, 2, 0, 3, 3, 3, 4, 3, 0, 2, 4, 5, 0, 3, 0, 3, 2, 3, 0, 3, 2, 2, 7, 3, 0, 2, 4, 3, 4, 5, 0, 2, 0, 5, 3, 5, 4, 1, 0, 5, 3, 2, 0, 3, 0, 3, 3, 2, 4, 1, 0, 3, 5, 6, 0, 1, 6, 4, 6, 4, 0, 1, 2, 5, 5, 6, 5, 4, 0, 3, 4, 3, 0, 4, 0, 7, 3

Offset

1,6

Comments

Number of nonleading 0-bits in A324712(n), with a(n) = 0 if A324712(n) = 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A324728(n) - A324829(n).

If A324712(n) > 0, then a(n) = -1 + A324734(n) + A324724(n).

a(p) = 0 for all primes p.

Prog

(PARI)
A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.
A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
A324735(n) = { my(k=A324712(n)); if(!k, k, 1 + (A000523(k)-hammingweight(k))); };

Crossrefs

Cf. A323243, A324712, A324728, A324733, A324829, A324724, A324734.

Sequence in context: A278500 A035211 A352558 * A219495 A242041 A376996

Adjacent sequences: A324732 A324733 A324734 * A324736 A324737 A324738

Keyword

nonn

Author

Antti Karttunen, Mar 17 2019

Status

approved