A262349 Sum of the divisors of the n-th Bell number.

1, 1, 3, 6, 24, 98, 240, 878, 13104, 34560, 143840, 1628640, 4421376, 27644438, 291751956, 1666163520, 10523628456, 216625138884, 779556556800, 5873176163328, 107021765366544, 633207380826720, 6399554302310400, 66975753492138600, 594616643557427040

Offset: 0

Author

Ilya Gutkovskiy, Sep 18 2015

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..104
• Eric Weisstein's World of Mathematics, Bell Number
• Eric Weisstein's World of Mathematics, Divisor Function

Crossrefs

Cf. A000110, A000203.

Programs

Magma

[DivisorSigma(1, Bell(n)): n in [0..30]]; // Vincenzo Librandi, Sep 19 2015

Mathematica

Table[DivisorSigma[1, BellB[n]], {n, 0, 22}]

PARI

a000110(n) = n! * polcoeff( exp( exp( x + x * O(x^n)) - 1), n);
vector(30, n, sigma(a000110(n-1))) \\ Altug Alkan, Sep 26 2015

PARI

a000110(n) = round(exp(-1)*suminf(k=0, 1.0*k^n/k!));
vector(30, n, sigma(a000110(n-1))) \\ Altug Alkan, Oct 04 2015

Formula

a(n) = sigma_1(A000110(n)) = A000203(A000110(n)).

a(n) = sigma_1(1/e*Sum_{k >=0} k^n/(k!)).

Extensions

More terms from Vincenzo Librandi, Sep 19 2015