A368817 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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