%I
%S 3,10,18,33,57,83,114,149,197,260,340,439,559,683,810,953,1121,1316,
%T 1531,1755,1997,2252,2540,2863,3205,3565,3964,4404,4887,5398,5926,
%U 6501,7125,7800,8528,9311,10151,11050,12010,13009,14032,15120,16275,17499
%N Partial sums of A045542.
%C Partial sums of subperfect powers: perfect powers (squares, cubes, etc.) minus 1. The subsequence of primes in the partial sum begins: 3, 83, 149, 197, 439, 683, 953, 1531, 1997, 9311, 10151, 13009. The subsequence of subperfect powers in the partial sum (numbers n such that n1 is a perfect power) begins: 10 (because 101=9=3^2), 197 because 1971=196=2^2 * 7^2.
%H Robert Israel, <a href="/A177955/b177955.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = SUM[i=1..n] A045542(i) = SUM[i=1..n] (A001597(i+1)  1) = (SUM[i=1..n] A001597(i+1))  n.
%e a(40) = 3 + 7 + 8 + 15 + 24 + 26 + 31 + 35 + 48 + 63 + 80 + 99 + 120 + 124 + 127 + 143 + 168 + 195 + 215 + 224 + 242 + 255 + 288 + 323 + 342 + 360 + 399 + 440 + 483 + 511 + 528 + 575 + 624 + 675 + 728 + 783 + 840 + 899 + 960 + 999 = 13009 is prime.
%p N:= 10^4:
%p P:= sort(convert({seq(seq(i^p1, p=2..floor(log[i](N))),i=2..isqrt(N))},list)):
%p ListTools:PartialSums(P); # _Robert Israel_, Jul 06 2017
%Y Cf. A001597, A045542.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, May 16 2010
