A324724 a(n) = A001511(A324712(n)), with a(n) = 0 if A324712(n) = 0.

0, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 2, 5, 1, 1, 1, 3, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 4, 2, 2, 2, 3, 1, 3, 3, 6, 1, 4, 1, 1, 1, 2, 1, 4, 1, 1, 8, 1, 1, 3, 1, 3, 3, 4, 1, 2, 1, 2, 3, 4, 2, 1, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 2, 1, 1, 4, 5, 2, 1, 1, 4, 2, 3, 4, 1, 1, 1, 1, 2, 2, 3, 5, 1, 4, 1, 2, 1, 1, 1, 8, 3

Offset

1,6

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

If A324712(n) = 0, then a(n) = 0, otherwise a(n) = A001511(A324712(n)).

a(p) = 1 for all primes p.

A324828(n) = [1 == a(n)], where [ ] is the Iverson bracket.

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.
A001511ext(n) = if(!n, n, sign(n)*(1+valuation(n, 2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
A324724(n) = A001511ext(A324712(n));

Crossrefs

Cf. A001511, A323243, A324543, A324712, A324725, A324810, A324828, A324829.

Sequence in context: A175623 A121273 A063065 * A051718 A370414 A016472

Adjacent sequences: A324721 A324722 A324723 * A324725 A324726 A324727

Keyword

nonn

Author

Antti Karttunen, Mar 17 2019

Status

approved