A366450 a(n) = Sum_{k=1..n} A366362(n,k)*A023900(k)/n.

1, -2, -1, -4, 1, 2, -2, -8, -3, -2, 1, 4, 4, 4, -1, -16, -2, 6, 0, -4, 2, -2, -1, 8, 5, -8, -9, 8, 0, 2, 7, -32, -1, 4, -2, 12, 3, 0, -4, -8, -8, -4, -6, -4, -3, 2, 8, 16, -14, -10, 2, -16, -6, 18, 1, 16, 0, 0, 5, 4, 12, -14, 6, -64, 4, 2, -7, 8, 1, 4, -3, 24, 4, -6, -5, 0, -2, 8, -10, -16, -27, 16, -6, -8

Offset

1,2

Comments

It appears that: a(A005117(n)) = A006571(A005117(n)), verified up to n = 98. But also a(76) = A006571(76), a(116) = A006571(116) and a(152) = A006571(152). 76 = 19*2^2, 116 = 29*2^2 and 152 = 19*2^3.

Links

Table of n, a(n) for n=1..84.

Formula

a(n) = Sum_{k=1..n} A366362(n,k)*A023900(k)/n.

Mathematica

nn = 84; f = x^3 - x^2 - y^2 - y; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Monitor[Table[Sum[Sum[Sum[If[GCD[f, n] == k, 1, 0]*g[k]/n, {x, 1, n}], {y, 1, n}], {k, 1, n}], {n, 1, nn}], n]

Prog

(PARI) a(n) = sum(k=1, n, my(z=sumdivmult(k, d, d*moebius(d))); sum(y=1, n, sum(x=1, n, if (gcd(x^3 - x^2 - y^2 - y, n)==k, z/n)))); \\ Michel Marcus, Oct 10 2023

Crossrefs

Cf. A366362, A023900, A006571, A005117, A002070, A366362.

Sequence in context: A070194 A323300 A349128 * A105584 A072064 A105498

Adjacent sequences: A366447 A366448 A366449 * A366451 A366452 A366453

Keyword

sign

Author

Mats Granvik, Oct 10 2023

Status

approved