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A368817
Sum of the refactorable numbers less than n that do not divide n.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 06 2024
STATUS
approved