A353233 Möbius transform of sigma_n(n).

1, 4, 27, 268, 3125, 47418, 823543, 16842736, 387440145, 10009763520, 285311670611, 8918294495628, 302875106592253, 11112685047823702, 437893920912783255, 18447025552964452096, 827240261886336764177, 39346558271491791438000, 1978419655660313589123979

Offset: 1

Author

Wesley Ivan Hurt, Jun 24 2022

Keywords

• nonn

Examples

			a(6) = 47418; a(6) = Sum_{d|6} sigma_d(d) * mu(6/d) = sigma_1(1) * mu(6/1) + sigma_2(2) * mu(6/2) + sigma_3(3) * mu(6/3) + sigma_6(6) * mu(6/6) = 1*1 + 5*(-1) + 28*(-1) + 47450*1 = 47418.
		

Links

• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A008683 (mu), A023887.

Programs

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[#, #]*MoebiusMu[n/#] &]; Array[a, 20] (* Wesley Ivan Hurt, Nov 12 2022 *)

PARI

a(n) = sumdiv(n, d, sigma(d,d)*moebius(n/d)); \\ Michel Marcus, Jun 24 2022

Formula

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