A308037 a(n) = Sum_{d|n} Stirling2(n,d).

1, 2, 2, 9, 2, 123, 2, 1830, 3027, 43038, 2, 2023728, 2, 49337473, 213142023, 2313595723, 2, 216927216877, 2, 6712023695345, 82312699558575, 366282502967439, 2, 113350450913387211, 2436684974110753, 1850568574287104493, 106563274551407600878, 231678790379913209098, 2

Offset: 1

Author

Ilya Gutkovskiy, May 10 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..579

Crossrefs

Cf. A000040, A008277, A056045, A096308.

Programs

Maple

a:= n-> add(Stirling2(n, d), d=numtheory[divisors](n)):
seq(a(n), n=1..30);  # Alois P. Heinz, May 10 2019

Mathematica

a[n_] := a[n] = Sum[StirlingS2[n, d], {d, Divisors[n]}]; Table[a[n], {n, 1, 29}]

PARI

a(n) = sumdiv(n, d, stirling(n, d, 2)); \\ Michel Marcus, May 10 2019

Formula

a(n) = 2 <=> n is prime <=> n in { A000040 }. - Alois P. Heinz, May 10 2019