A122616 Sums of 5th powers of primes.

32, 64, 96, 128, 160, 192, 224, 243, 256, 275, 288, 307, 320, 339, 352, 371, 384, 403, 416, 435, 448, 467, 480, 486, 499, 512, 518, 531, 544, 550, 563, 576, 582, 595, 608, 614, 627, 640, 646, 659, 672, 678, 691, 704, 710, 723, 729, 736, 742, 755, 761, 768

Offset

1,1

Comments

After a finite number of integers which cannot be written as a sum of 5th powers of primes, all integers can be so written.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

a(n) = a*32 + b*243 + c*3125 + d*16807 + e*161051 + ... where a,b,c,d,e,... are nonnegative integers. Sumset of A050997 Fifth powers of primes.

Mathematica

ok[n_] := {} != Quiet@ IntegerPartitions[n, All, Prime[ Range@ PrimePi@ Max[2, n^(1/5)]]^5, 1]; Select[Range[768], ok] (* Giovanni Resta, Jun 12 2016 *)

Crossrefs

Cf. A000040, A050997.

Sequence in context: A116318 A225722 A195330 * A174312 A255995 A144908

Adjacent sequences: A122613 A122614 A122615 * A122617 A122618 A122619

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 21 2006

Extensions

Several missing terms from Giovanni Resta, Jun 12 2016

Status

approved