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%I #11 May 11 2019 02:13:26
%S 1,2,2,9,2,123,2,1830,3027,43038,2,2023728,2,49337473,213142023,
%T 2313595723,2,216927216877,2,6712023695345,82312699558575,
%U 366282502967439,2,113350450913387211,2436684974110753,1850568574287104493,106563274551407600878,231678790379913209098,2
%N a(n) = Sum_{d|n} Stirling2(n,d).
%F a(n) = 2 <=> n is prime <=> n in { A000040 }. - _Alois P. Heinz_, May 10 2019
%p a:= n-> add(Stirling2(n, d), d=numtheory[divisors](n)):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, May 10 2019
%t a[n_] := a[n] = Sum[StirlingS2[n, d], {d, Divisors[n]}]; Table[a[n], {n, 1, 29}]
%o (PARI) a(n) = sumdiv(n, d, stirling(n, d, 2)); \\ _Michel Marcus_, May 10 2019
%Y Cf. A000040, A008277, A056045, A096308.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, May 10 2019
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