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A345140
a(1) = 1; a(n+1) = n + Sum_{d|n} a(d).
0
1, 2, 5, 9, 16, 22, 36, 44, 64, 79, 108, 120, 171, 185, 238, 275, 347, 365, 477, 497, 624, 687, 820, 844, 1071, 1113, 1313, 1410, 1671, 1701, 2094, 2126, 2489, 2636, 3020, 3108, 3732, 3770, 4288, 4504, 5192, 5234, 6151, 6195, 7046, 7415, 8284, 8332, 9702, 9788, 11007, 11411, 12759, 12813, 14639
OFFSET
1,2
FORMULA
G.f. A(x) satisfies: A(x) = x * (1 + x / (1 - x)^2 + A(x) + A(x^2) + A(x^3) + ...).
MATHEMATICA
a[1] = 1; a[n_] := a[n] = n - 1 + Sum[a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 55}]
nmax = 55; A[_] = 0; Do[A[x_] = x (1 + x/(1 - x)^2 + Sum[A[x^k], {k, 1, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 09 2021
STATUS
approved