

A124405


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


4



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

1,1


COMMENTS

p divides a(p) and a(p1) 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(p1) 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


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)/(j1).
a(n) = A086787(n) + 1.


MAPLE

seq( n+1+add(j*(j^n1)/(j1), 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}]


PROG

(PARI) vector(30, n, n+1 + sum(j=2, n, j*(j^n1)/(j1)) ) \\ G. C. Greubel, Dec 25 2019
(MAGMA) [0] cat [n+1 + (&+[j*(j^n1)/(j1): j in [2..n]]): n in [2..30]]; // G. C. Greubel, Dec 25 2019
(Sage) [n+1 + sum(j*(j^n1)/(j1) for j in (2..n)) for n in (1..30)] # G. C. Greubel, Dec 25 2019
(GAP) List([1..30], n> n+1 + Sum([2..n], j> j*(j^n1)/(j1)) ); # G. C. Greubel, Dec 25 2019


CROSSREFS

Cf. A007540, A079853, A086787.
Sequence in context: A218824 A111545 A070075 * A300343 A141787 A047852
Adjacent sequences: A124402 A124403 A124404 * A124406 A124407 A124408


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Dec 14 2006


EXTENSIONS

Edited by Max Alekseyev, Jan 29 2012


STATUS

approved



