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

Author

Jonathan Vos Post, Sep 21 2006

Keywords

• easy
• nonn

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

Crossrefs

Cf. A000040, A050997.

Programs

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 *)

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.

Extensions

Several missing terms from Giovanni Resta, Jun 12 2016