A133298 a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} i^(j+k).

2, 41, 1727, 130917, 17245160, 3546873073, 1046002784253, 417182980579609, 215861313302976046, 140463714074395109081, 112191246261394235358555, 107867952671976721983260413, 122856922623618324408724634164

Offset: 1

Author

Alexander Adamchuk, Oct 17 2007

Keywords

• nonn

Comments

p divides a(p) for prime p>3. p^2 divides a(p) for prime p=7. Nonprime n dividing a(n) are {1,15}.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A124405.

Cf. A062970, A086787.

Programs

GAP

List([1..20], n-> 1 + n^2 + Sum([2..n], j-> (j*(j^n-1)/(j-1))^2) ); # G. C. Greubel, Aug 02 2019

Magma

[2] cat [1+n^2 + (&+[(j*(j^n-1)/(j-1))^2: j in [2..n]]): n in [1..20]]; // G. C. Greubel, Aug 02 2019

Mathematica

Table[Sum[(i(i^n-1)/(i-1))^2, {i,2,n}] +n^2 +1,{n,20}]

PARI

vector(20, n, 1+n^2 + sum(j=2,n, (j*(j^n-1)/(j-1))^2)) \\ G. C. Greubel, Aug 02 2019

Sage

[1+n^2 + sum((j*(j^n-1)/(j-1))^2 for j in (2..n)) for n in (1..20)] # G. C. Greubel, Aug 02 2019

Formula

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

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