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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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.

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}]

PROG

(PARI) vector(30, n, n+1 + sum(j=2, n, 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

(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

(GAP) List([1..30], n-> n+1 + Sum([2..n], j-> j*(j^n-1)/(j-1)) ); # 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

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Last modified July 24 00:28 EDT 2021. Contains 346265 sequences. (Running on oeis4.)