A368818 Number of balanced numbers less than n that do not divide n.

0, 0, 1, 1, 2, 0, 3, 2, 2, 2, 3, 0, 4, 3, 4, 5, 6, 3, 6, 5, 5, 5, 6, 2, 6, 5, 5, 4, 6, 2, 7, 6, 6, 6, 7, 4, 8, 7, 7, 7, 8, 4, 9, 8, 7, 8, 9, 5, 9, 8, 8, 8, 9, 6, 9, 7, 9, 9, 10, 4, 10, 9, 9, 9, 10, 7, 10, 9, 9, 7, 11, 7, 11, 10, 9, 10, 11, 8, 12, 11, 11, 11, 12, 6, 12

Offset

1,5

Links

Table of n, a(n) for n=1..85.

Formula

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

Example

a(15) = 4 since there are 4 balanced numbers less than 15 that do not divide 15, namely: 2, 6, 12, 14.

Mathematica

Table[Sum[(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, A368819.

Sequence in context: A100949 A152164 A263112 * A110493 A118234 A262771

Adjacent sequences: A368815 A368816 A368817 * A368819 A368820 A368821

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 06 2024

Status

approved