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A122616 Sums of 5th powers of primes. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 21 13:21 EDT 2017. Contains 290890 sequences.