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

2, 9, 57, 495, 5700, 82201, 1419761, 28501117, 651233662, 16676686697, 472883843993, 14705395791307, 497538872883728, 18193397941038737, 714950006521386977, 30046260016074301945, 1344648068888240941018

Offset: 1

Author

Alexander Adamchuk, Dec 14 2006

Keywords

• nonn

Comments

p divides a(p) and a(p-1) for prime p.

p^2 divides a(p) for prime p in {5, 13, 563, ...} which seems to coincide with the Wilson primes (A007540).

p^2 divides a(p-1) for prime p in {3, 11, 107, ...} which seems to coincide with the odd primes in A079853.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..385

Crossrefs

Cf. A007540, A079853, A086787.

Programs

GAP

List([1..30], n-> n+1 + Sum([2..n], j-> j*(j^n-1)/(j-1)) ); # G. C. Greubel, Dec 25 2019

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

Maple

seq( n+1+add(j*(j^n-1)/(j-1), j=2..n), n=1..30); # G. C. Greubel, Dec 25 2019

Mathematica

Table[Sum[i^j,{i,1,n},{j,1,n}]+1,{n,1,20}]

PARI

vector(30, n, n+1 + sum(j=2,n, j*(j^n-1)/(j-1)) ) \\ G. C. Greubel, Dec 25 2019

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

Formula

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

a(n) = n + 1 + Sum_{j=2..n} j*(j^n - 1)/(j-1).

a(n) = A086787(n) + 1.

Extensions

Edited by Max Alekseyev, Jan 29 2012