A378651 a(n) = 1 if the divisors of n can be partitioned in exactly two ways into two disjoint sets with the same sum, otherwise 0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..108045

Index entries for characteristic functions

Formula

a(n) = [A083206(n) = 2], where [ ] is the Iverson bracket.

Prog

(PARI)
A083206(n) = { my(s=sigma(n), p=1); if(s%2 || s < 2*n, 0, fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2)); };
A378651(n) = (2==A083206(n));

Crossrefs

Characteristic function of A378652.

Cf. A083206.

Sequence in context: A297046 A248805 A307721 * A023976 A025469 A025466

Adjacent sequences: A378648 A378649 A378650 * A378652 A378653 A378654

Keyword

nonn

Author

Antti Karttunen, Dec 02 2024

Status

approved