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A177955 Partial sums of A045542. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 15 01:07 EST 2019. Contains 329142 sequences. (Running on oeis4.)