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A338749
a(0) = 1; for n > 0, a(n) = n * Sum_{d|n, d < n} a(d - 1) / d.
0
1, 0, 2, 3, 4, 5, 10, 7, 14, 15, 18, 11, 39, 13, 34, 37, 42, 17, 73, 19, 81, 65, 58, 23, 121, 45, 104, 87, 115, 29, 212, 31, 158, 109, 118, 113, 240, 37, 184, 182, 235, 41, 366, 43, 279, 283, 162, 47, 399, 119, 407, 211, 337, 53, 478, 189, 453, 314, 288, 59, 639
OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 1 + 2 * x^2 * A(x^2) + 3 * x^3 * A(x^3) + 4 * x^4 * A(x^4) + ...
MATHEMATICA
a[0] = 1; a[n_] := a[n] = n DivisorSum[n, a[# - 1]/# &, # < n &]; Table[a[n], {n, 0, 60}]
nmax = 60; A[_] = 0; Do[A[x_] = 1 + Sum[k x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 06 2020
STATUS
approved