A081175 Numbers of the form Sum_{i=1..k} i^j, j >= 1, k >= 1.

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

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

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

Cf. A000217, A000330, A000537, A000538, A000539, A000540, A000541, A000542, A007487, A023002.

For primes in this sequence see A164307.

Sequence in context: A167384 A112649 A050083 * A269110 A182050 A094598

Adjacent sequences: A081172 A081173 A081174 * A081176 A081177 A081178

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