A386592 Sum of the divisors of n that are not balanced numbers.

0, 0, 0, 4, 5, 0, 7, 12, 9, 15, 11, 4, 13, 7, 5, 28, 17, 27, 19, 39, 28, 33, 23, 36, 30, 39, 36, 39, 29, 15, 31, 60, 44, 51, 12, 67, 37, 57, 52, 87, 41, 28, 43, 81, 59, 69, 47, 100, 56, 90, 68, 95, 53, 108, 71, 47, 76, 87, 59, 99, 61, 93, 100, 124, 83, 132, 67, 123, 92, 22, 71, 171, 73, 111, 105, 137, 95, 78, 79, 183, 117, 123, 83, 144, 107, 129, 116, 177

Offset

1,4

Comments

Sum of the divisors d of n such that phi(d) does not divide sigma(d).

Inverse Möbius transform of n * (1 - c(n)), where c = A351114.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n} d * (1 - c(d)), where c = A351114.

a(n) = A000203(n) - A351113(n).

Maple

g:= proc(n) option remember; numtheory:-sigma(n) mod numtheory:-phi(n) <> 0 end proc:
f:= n -> convert(select(g, numtheory:-divisors(n)), `+`):
map(f, [$1..100]); # Robert Israel, Aug 26 2025

Mathematica

Table[Sum[d (Ceiling[DivisorSigma[1, d]/EulerPhi[d]] - Floor[DivisorSigma[1, d]/EulerPhi[d]]), {d, Divisors[n]}], {n, 100}]

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A351113, A351114, A387333.

Sequence in context: A318740 A240160 A249860 * A360962 A320162 A388881

Adjacent sequences: A386589 A386590 A386591 * A386593 A386594 A386595

Keyword

nonn,look

Author

Wesley Ivan Hurt, Jul 26 2025

Status

approved