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

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

Cf. A033950, A336040, A368817.

Sequence in context: A331614 A343541 A060025 * A067399 A106737 A359360

Adjacent sequences: A368569 A368570 A368571 * A368573 A368574 A368575

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 06 2024

Status

approved