A123269 Sum[ i^j^k, {i,1,n}, {j,1,n}, {k,1,n} ].

1, 28, 7625731729896, 13407807929942597099574024998205985135931742965325158317510351105024878248924471298029103219186757034747676158536830429928105045387310278568778808509188348

Offset: 1

Author

Alexander Adamchuk, Oct 09 2006

Keywords

• nonn

Comments

The next term is too large to include.

Prime p divides a(p) for p = {2, 3, 7, 11, 23, 31, 43, 47, 59, 67, 71, 79, ...} = A039787[n] Primes p such that p-1 is squarefree. p^2 divides a(p) for prime p = {2,3}.

Crossrefs

Cf. A039787. Cf. A086787 - Sum[ i^j, {i, 1, n}, {j, 1, n} ].

Numbers n that divide a(n) are listed in A124391(n) = {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 21, 22, 23, 24, 27, 28, 31, ...}.

Programs

Mathematica

Table[Sum[i^j^k,{i,1,n},{j,1,n},{k,1,n}],{n,1,5}]

PARI

a(n)=sum(i=1,n,sum(j=1,n,sum(k=1,n,i^j^k))) \\ Charles R Greathouse IV, May 15 2013

Formula

a(n) = Sum[ i^j^k, {i,1,n}, {j,1,n}, {k,1,n} ].