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A307502
Self-convolution of the Dedekind psi function (A001615).
0
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 11 2019
STATUS
approved