A133298 - OEIS

%I #6 Sep 08 2022 08:45:31

%S 2,41,1727,130917,17245160,3546873073,1046002784253,417182980579609,

%T 215861313302976046,140463714074395109081,112191246261394235358555,

%U 107867952671976721983260413,122856922623618324408724634164

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

%C 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}.

%H G. C. Greubel, <a href="/A133298/b133298.txt">Table of n, a(n) for n = 1..210</a>

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

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

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

%o (PARI) vector(20, n, 1+n^2 + sum(j=2,n, (j*(j^n-1)/(j-1))^2)) \\ _G. C. Greubel_, Aug 02 2019

%o (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

%o (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

%o (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

%Y Cf. A124405.

%Y Cf. A062970, A086787.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Oct 17 2007