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A133298
a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} i^(j+k).
1
2, 41, 1727, 130917, 17245160, 3546873073, 1046002784253, 417182980579609, 215861313302976046, 140463714074395109081, 112191246261394235358555, 107867952671976721983260413, 122856922623618324408724634164
OFFSET
1,1
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
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.
MATHEMATICA
Table[Sum[(i(i^n-1)/(i-1))^2, {i, 2, n}] +n^2 +1, {n, 20}]
PROG
(PARI) vector(20, n, 1+n^2 + sum(j=2, n, (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
(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
(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
CROSSREFS
Cf. A124405.
Sequence in context: A176941 A240553 A129208 * A054742 A113634 A098634
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Oct 17 2007
STATUS
approved