A378446 Inverse Möbius transform of A083206, where A083206(n) is the number of ways of partitioning the divisors of n into two disjoint sets with equal sum.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 23, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 3, 0, 6, 0, 0, 0, 19, 0, 0, 0, 1, 0, 17, 0, 0, 0, 0, 0, 21, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 12

Offset: 1

Author

Antti Karttunen, Nov 28 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A083206.

Programs

PARI

A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };
A378446(n) = sumdiv(n,d,A083206(d));

Formula

a(n) = Sum_{d|n} A083206(d).