A361709 Moebius transform of nonprimes.

1, 3, 5, 4, 8, 1, 11, 6, 9, 4, 17, 6, 20, 7, 10, 11, 25, 8, 27, 10, 15, 12, 33, 9, 27, 14, 24, 14, 41, 12, 44, 21, 25, 20, 30, 14, 51, 23, 29, 20, 56, 15, 59, 25, 30, 27, 64, 20, 56, 26, 39, 30, 73, 24, 50, 31, 45, 35, 80, 18, 83, 37, 45, 41, 59, 26, 90, 39, 54, 30

Offset: 1

Author

Ilya Gutkovskiy, Mar 21 2023

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A007444, A018252, A361708.

Programs

Mathematica

With[{np = Select[Range[100], !PrimeQ[#] &]}, Table[DivisorSum[n, MoebiusMu[n/#]*np[[#]] &], {n, Length[np]}]] (* Paolo Xausa, Aug 21 2025 *)

Formula

a(n) = Sum_{d|n} mu(n/d) * A018252(d).