cp's OEIS Frontend

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

%I A262349 #31 Feb 16 2025 08:33:27
%S A262349 1,1,3,6,24,98,240,878,13104,34560,143840,1628640,4421376,27644438,
%T A262349 291751956,1666163520,10523628456,216625138884,779556556800,
%U A262349 5873176163328,107021765366544,633207380826720,6399554302310400,66975753492138600,594616643557427040
%N A262349 Sum of the divisors of the n-th Bell number.
%H A262349 Amiram Eldar, <a href="/A262349/b262349.txt">Table of n, a(n) for n = 0..104</a>
%H A262349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellNumber.html">Bell Number</a>
%H A262349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>
%F A262349 a(n) = sigma_1(A000110(n)) = A000203(A000110(n)).
%F A262349 a(n) = sigma_1(1/e*Sum_{k >=0} k^n/(k!)).
%t A262349 Table[DivisorSigma[1, BellB[n]], {n, 0, 22}]
%o A262349 (Magma) [DivisorSigma(1, Bell(n)): n in [0..30]]; // _Vincenzo Librandi_, Sep 19 2015
%o A262349 (PARI) a000110(n) = n! * polcoeff( exp( exp( x + x * O(x^n)) - 1), n);
%o A262349 vector(30, n, sigma(a000110(n-1))) \\ _Altug Alkan_, Sep 26 2015
%o A262349 (PARI) a000110(n) = round(exp(-1)*suminf(k=0, 1.0*k^n/k!));
%o A262349 vector(30, n, sigma(a000110(n-1))) \\ _Altug Alkan_, Oct 04 2015
%Y A262349 Cf. A000110, A000203.
%K A262349 nonn
%O A262349 0,3
%A A262349 _Ilya Gutkovskiy_, Sep 18 2015
%E A262349 More terms from _Vincenzo Librandi_, Sep 19 2015