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

Author

Wesley Ivan Hurt, Jan 06 2024

Keywords

• nonn
• easy

Examples

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

Crossrefs

Cf. A033950, A336040, A368817.

Programs

Mathematica

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

Formula

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