|
|
A353233
|
|
Möbius transform of sigma_n(n).
|
|
1
|
|
|
1, 4, 27, 268, 3125, 47418, 823543, 16842736, 387440145, 10009763520, 285311670611, 8918294495628, 302875106592253, 11112685047823702, 437893920912783255, 18447025552964452096, 827240261886336764177, 39346558271491791438000, 1978419655660313589123979
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{d|n} sigma_d(d) * mu(n/d).
|
|
EXAMPLE
|
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.
|
|
MATHEMATICA
|
a[n_] := DivisorSum[n, DivisorSigma[#, #]*MoebiusMu[n/#] &]; Array[a, 20] (* Wesley Ivan Hurt, Nov 12 2022 *)
|
|
PROG
|
(PARI) a(n) = sumdiv(n, d, sigma(d, d)*moebius(n/d)); \\ Michel Marcus, Jun 24 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|