A197953 -id:A197953 - cp's OEIS frontend

A318372 a(1) = 1; a(n+1) = Sum_{d|n} d*a(d).

1, 1, 3, 10, 43, 216, 1308, 9157, 73299, 659701, 6597228, 72569509, 870835456, 11320860929, 158492062165, 2377380932700, 38038094996499, 646647614940484, 11639657069589711, 221153484322204510, 4423069686450687468, 92884463415464445994, 2043458195140290381379, 46999538488226678771718

Offset: 1

Ilya Gutkovskiy, Aug 24 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..450

Cf. A003238, A038046, A197953.

f:= proc(n) option remember;
add(d*procname(d),d=numtheory:-divisors(n-1))
end proc:
f(1):= 1:
map(f, [$1..30]); # Robert Israel, Aug 24 2018

a[n_] := a[n] = Sum[d a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 24}]

a(n) = if (n==1, 1, sumdiv(n-1, d, d*a(d))); \\ Michel Marcus, Aug 25 2018

L.g.f.: -log(Product_{n>=1} (1 - x^n)^a(n)) = Sum_{n>=1} a(n+1)*x^n/n.

a(n) ~ c * (n-1)!, where c = 1.818022128135673369551657167939033389270758547856526032865616543756614556559... - Vaclav Kotesovec, Aug 25 2018

A307607 a(n) = 1 + Sum_{d|n, d > 1} d^2*a(n/d).

Original entry on oeis.org

1, 5, 10, 37, 26, 122, 50, 293, 172, 330, 122, 1306, 170, 642, 710, 2341, 290, 2876, 362, 3562, 1382, 1578, 530, 13082, 1276, 2202, 3088, 6946, 842, 12822, 962, 18725, 3398, 3762, 3750, 37756, 1370, 4698, 4742, 35818, 1682, 25014, 1850, 17098, 17072, 6882

Offset: 1

Ilya Gutkovskiy, Apr 18 2019

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A074206, A197953, A307604.

a[n_] := a[n] = 1 + DivisorSum[n, #^2 a[n/#] &, # > 1 &]; Table[a[n], {n, 1, 46}]

a(n) = 1 + sumdiv(n, d, if (d>1, d^2*a(n/d))); \\ Michel Marcus, Apr 20 2019

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k*A074206(k))) = Sum_{n>=1} a(n)*x^n/n.

cp's OEIS Frontend

A318372 a(1) = 1; a(n+1) = Sum_{d|n} d*a(d).

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