A324725 a(n) = sign(A324543(n)) * A001511(A324543(n)), with a(n) = 0 if A324543(n) = 0.

0, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 4, 5, 1, -1, 1, 3, 1, 5, 1, 4, 1, 3, 3, 1, 1, 2, 1, 4, 3, 5, 3, 3, 1, 2, 2, 6, 1, -2, 1, 1, 1, 6, 1, 4, 1, -1, 2, 1, 1, 3, 1, 3, 2, 2, 1, 2, 1, 5, 3, 4, 4, 1, 1, 1, 3, -4, 1, 3, 1, 3, 1, 1, 3, -1, 1, 4, 5, 5, 1, 1, 2, 4, 2, 4, 1, 1, 1, 1, 7, 5, 2, 7, 1, -2, 1, 2, 1, 1, 1, 8, 2

Offset: 1

Author

Antti Karttunen, Mar 17 2019

Keywords

• sign

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)

Crossrefs

Cf. A001511, A324343, A324543, A324724, A324817, A324828.

Programs

PARI

A324543(n) = sumdiv(n,d,moebius(n/d)*A323243(d));
A001511ext(n) = if(!n,n,sign(n)*(1+valuation(n,2))); \\ Like A001511 but gives 0 for 0 and -A001511(-n) for negative numbers.
A324725(n) = A001511ext(A324543(n));

Formula

If A324543(n) = 0, then a(n) = 0, otherwise a(n) = sign(A324543(n)) * A001511(A324543(n)).

a(p) = 1 for all primes p.

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