cp's OEIS Frontend

A120929 Partial sums of n^(n^2), A002489.

%I A120929 #11 Aug 23 2022 09:45:22
%S A120929 1,2,18,19701,4294986997,298023228171940122,
%T A120929 10314424798788558774343889178,
%U A120929 256923577521069192513410265783009965210785,6277101735386681020759366944276858929512621227473999723681
%N A120929 Partial sums of n^(n^2), A002489.
%C A120929 After 2, can this ever be prime? This is to A001923 Sum k^k, k=1..n, as k^k^k is to k^k.
%H A120929 Seiichi Manyama, <a href="/A120929/b120929.txt">Table of n, a(n) for n = 0..26</a>
%F A120929 a(n) = Sum_{i=0..n} i^(i^2). a(n) = Sum_{i=0..n} (i^i)^i. In this sequence, we formally define 0^0 = 1.
%e A120929 a(0) = 1 because A002489(0) is given formally as 0^0^0 = 1.
%e A120929 a(1) = 2 because 1 + (1^1)^1 = 1 + 1 = 2.
%e A120929 a(2) = 18 because 2 + (2^2)^2 = 2 + 16 = 18.
%e A120929 a(3) = 19701 because 18 + (3^3)^3 = 18 + 19683 = 19701.
%e A120929 a(4) = 4294986997 = 19701 + (4^4)^4 = 19701 + 4294967296.
%t A120929 Accumulate[Join[{1},Table[n^(n^2),{n,9}]]] (* _Harvey P. Dale_, Apr 10 2014 *)
%Y A120929 Cf. A001923, A002489, A002488, A001329, A002488, A023813, A076113, A090588.
%K A120929 easy,nonn
%O A120929 0,2
%A A120929 _Jonathan Vos Post_, Aug 18 2006
%E A120929 More terms from _Harvey P. Dale_, Apr 10 2014