A307502 - OEIS

A307502

Self-convolution of the Dedekind psi function (A001615).

0, 1, 6, 17, 36, 64, 108, 172, 240, 340, 444, 612, 744, 980, 1164, 1504, 1704, 2172, 2388, 2964, 3288, 3968, 4272, 5272, 5520, 6624, 7104, 8276, 8640, 10404, 10572, 12480, 13032, 14988, 15300, 18204, 18048, 21004, 21636, 24616, 24648, 29036, 28452, 32768, 33552, 37488

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..46.

Eric Weisstein's World of Mathematics, Dedekind Function

FORMULA

G.f.: (Sum_{k>=1} mu(k)^2*x^k/(1 - x^k)^2)^2.

a(n) = Sum_{k=1..n-1} A001615(k)*A001615(n-k).

MATHEMATICA

Rest[nmax = 46; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k/(1 - x^k)^2, {k, 1, nmax}]^2, {x, 0, nmax}], x]]

psi[n_] := psi[n] = Sum[MoebiusMu[n/d]^2 d, {d, Divisors @ n}]; a[n_] := a[n] = Sum[psi[k] psi[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 46}]