[go: up one dir, main page]

login
A081175
Numbers of the form Sum_{i=1..k} i^j, j >= 1, k >= 1.
2
1, 3, 5, 6, 9, 10, 14, 15, 17, 21, 28, 30, 33, 36, 45, 55, 65, 66, 78, 91, 98, 100, 105, 120, 129, 136, 140, 153, 171, 190, 204, 210, 225, 231, 253, 257, 276, 285, 300, 325, 351, 354, 378, 385, 406, 435, 441, 465, 496, 506, 513, 528, 561, 595, 630, 650, 666, 703
OFFSET
1,2
COMMENTS
Union of sums of k-th powers, for k >= 1.
LINKS
Michael Penn, an excruciatingly deep dive into the power sum., YouTube video, 2022.
EXAMPLE
30 is in the set because 30 = 1^2 + 2^2 + 3^2 + 4^2 (j=2, k=4).
MAPLE
N:= 1000: # to get all terms <= N
A:=select(`<=`, {1, seq(seq(sum(i^k, i=1..m), m=2..floor((N*(k+1))^(1/(k+1)))), k = 1 ..ilog2(N-1))}, N):
sort(convert(A, list)); # Robert Israel, Jan 26 2015
MATHEMATICA
Take[ Union[ Flatten[ Table[ Sum[ i^j, {i, 1, n}], {j, 1, 9}, {n, 1, 40}]]], 60]
CROSSREFS
For primes in this sequence see A164307.
Sequence in context: A167384 A112649 A050083 * A269110 A182050 A094598
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 18 2003
EXTENSIONS
Corrected and extended by Robert G. Wilson v, May 08 2003
STATUS
approved