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

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

1,2

Links

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

Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Formula

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

From Vaclav Kotesovec, Jul 09 2026: (Start)

Dirichlet g.f.: zeta(s)/(2 - zeta(s-2)).

Sum_{k=1..n} a(k) ~ zeta(r)^2 * n^r / (r*((zeta(r-2) - 2)*zeta'(r) - zeta(r)*zeta'(r-2))), where r = A107311 + 2 = 3.728647238998183618135103010297691464234109849335... is the root of the equation zeta(r-2) = 2. (End)

Mathematica

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

Prog

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

Crossrefs

Cf. A074206, A197953, A307604, A107311.

Sequence in context: A032772 A326232 A189732 * A174933 A392237 A270219

Adjacent sequences: A307604 A307605 A307606 * A307608 A307609 A307610

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Apr 18 2019

Status

approved