A177955 Partial sums of A045542.

3, 10, 18, 33, 57, 83, 114, 149, 197, 260, 340, 439, 559, 683, 810, 953, 1121, 1316, 1531, 1755, 1997, 2252, 2540, 2863, 3205, 3565, 3964, 4404, 4887, 5398, 5926, 6501, 7125, 7800, 8528, 9311, 10151, 11050, 12010, 13009, 14032, 15120, 16275, 17499

Offset

1,1

Comments

Partial sums of sub-perfect 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 n-1 is a perfect power) begins: 10 (because 10-1=9=3^2), 197 because 197-1=196=2^2 * 7^2.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = SUM[i=1..n] A045542(i) = SUM[i=1..n] (A001597(i+1) - 1) = (SUM[i=1..n] A001597(i+1)) - n.

Example

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.

Maple

N:= 10^4:
P:= sort(convert({seq(seq(i^p-1, p=2..floor(log[i](N))), i=2..isqrt(N))}, list)):
ListTools:-PartialSums(P); # Robert Israel, Jul 06 2017

Crossrefs

Cf. A001597, A045542.

Sequence in context: A171834 A210286 A275988 * A298976 A265487 A074893

Adjacent sequences: A177952 A177953 A177954 * A177956 A177957 A177958

Keyword

easy,nonn

Author

Jonathan Vos Post, May 16 2010

Status

approved