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

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}]

Crossrefs

Cf. A001615, A008683, A065093, A307309.

Sequence in context: A083045 A012277 A358245 * A084990 A024181 A023663

Adjacent sequences: A307499 A307500 A307501 * A307503 A307504 A307505

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 11 2019

Status

approved