A368572 - OEIS

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A368572

Number of refactorable numbers less than n that do not divide n.

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

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OFFSET

1,9

LINKS

Table of n, a(n) for n=1..84.

FORMULA

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

EXAMPLE

a(15) = 4 since there are 4 refactorable numbers that are less than 15 and do not divide 15, namely: 2, 8, 9, 12.

MATHEMATICA

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

CROSSREFS