A368819 Sum of the balanced numbers less than n that do not divide n.

0, 0, 2, 3, 5, 0, 11, 9, 8, 9, 11, 0, 23, 21, 34, 50, 52, 41, 52, 50, 49, 50, 52, 29, 52, 50, 49, 36, 52, 26, 82, 80, 79, 80, 82, 94, 117, 115, 114, 115, 117, 92, 159, 157, 141, 157, 159, 136, 159, 157, 156, 157, 159, 148, 159, 143, 212, 213, 215, 147, 215, 213, 212

Offset

1,3

Links

Table of n, a(n) for n=1..63.

Formula

a(n) = Sum_{k=1..n} k * c(k) * (ceiling(n/k) - floor(n/k)), where c = A351114.

Example

a(15) = 34. There are 4 balanced numbers less than 15 that do not divide 15, namely: 2, 6, 12, 14. Their sum is 2 + 6 + 12 + 14 = 34.

Mathematica

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

Crossrefs

Cf. A020492, A351114, A368818.

Sequence in context: A126047 A023049 A240979 * A171034 A062007 A031067

Adjacent sequences: A368816 A368817 A368818 * A368820 A368821 A368822

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 06 2024

Status

approved