cp's OEIS Frontend

A124405 a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} i^j.

%I A124405 #11 Sep 08 2022 08:45:28
%S A124405 2,9,57,495,5700,82201,1419761,28501117,651233662,16676686697,
%T A124405 472883843993,14705395791307,497538872883728,18193397941038737,
%U A124405 714950006521386977,30046260016074301945,1344648068888240941018
%N A124405 a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} i^j.
%C A124405 p divides a(p) and a(p-1) for prime p.
%C A124405 p^2 divides a(p) for prime p in {5, 13, 563, ...} which seems to coincide with the Wilson primes (A007540).
%C A124405 p^2 divides a(p-1) for prime p in {3, 11, 107, ...} which seems to coincide with the odd primes in A079853.
%H A124405 G. C. Greubel, <a href="/A124405/b124405.txt">Table of n, a(n) for n = 1..385</a>
%F A124405 a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} i^j.
%F A124405 a(n) = n + 1 + Sum_{j=2..n} j*(j^n - 1)/(j-1).
%F A124405 a(n) = A086787(n) + 1.
%p A124405 seq( n+1+add(j*(j^n-1)/(j-1), j=2..n), n=1..30); # _G. C. Greubel_, Dec 25 2019
%t A124405 Table[Sum[i^j,{i,1,n},{j,1,n}]+1,{n,1,20}]
%o A124405 (PARI) vector(30, n, n+1 + sum(j=2,n, j*(j^n-1)/(j-1)) ) \\ _G. C. Greubel_, Dec 25 2019
%o A124405 (Magma) [0] cat [n+1 + (&+[j*(j^n-1)/(j-1): j in [2..n]]): n in [2..30]]; // _G. C. Greubel_, Dec 25 2019
%o A124405 (Sage) [n+1 + sum(j*(j^n-1)/(j-1) for j in (2..n)) for n in (1..30)] # _G. C. Greubel_, Dec 25 2019
%o A124405 (GAP) List([1..30], n-> n+1 + Sum([2..n], j-> j*(j^n-1)/(j-1)) ); # _G. C. Greubel_, Dec 25 2019
%Y A124405 Cf. A007540, A079853, A086787.
%K A124405 nonn
%O A124405 1,1
%A A124405 _Alexander Adamchuk_, Dec 14 2006
%E A124405 Edited by _Max Alekseyev_, Jan 29 2012