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

0,3

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000110, A000203.

Sequence in context: A296215 A152761 A295761 * A109155 A338112 A294381

Adjacent sequences: A262346 A262347 A262348 * A262350 A262351 A262352

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 18 2015

Extensions

More terms from Vincenzo Librandi, Sep 19 2015

Status

approved