A368817 Sum of the refactorable numbers less than n that do not divide n.

0, 0, 2, 0, 2, 0, 2, 0, 10, 17, 19, 17, 31, 29, 31, 21, 31, 20, 49, 47, 49, 47, 49, 27, 73, 71, 64, 71, 73, 71, 73, 63, 73, 71, 73, 32, 109, 107, 109, 99, 149, 147, 149, 147, 140, 147, 149, 103, 149, 147, 149, 147, 149, 120, 149, 139, 205, 203, 205, 191, 265, 263

Offset

1,3

Links

Table of n, a(n) for n=1..62.

Formula

a(n) = Sum_{k=1..n} k * c(k) * (ceiling(n/k) - floor(n/k)), where c = A336040.

Example

a(15) = 31. There are 4 refactorable numbers that are less than 15 that do not divide 15, namely: 2, 8, 9, 12. Their sum is 2 + 8 + 9 + 12 = 31.

Mathematica

Table[Sum[k (1 - Ceiling[k/DivisorSigma[0, k]] + Floor[k/DivisorSigma[0, k]]) (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}]

Crossrefs

Cf. A033950, A336040, A368572.

Sequence in context: A307692 A300548 A293898 * A324301 A361235 A243822

Adjacent sequences: A368814 A368815 A368816 * A368818 A368819 A368820

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 06 2024

Status

approved