A122614 Sums of 4th powers of primes.

16, 32, 48, 64, 80, 81, 96, 97, 112, 113, 128, 129, 144, 145, 160, 161, 162, 176, 177, 178, 192, 193, 194, 208, 209, 210, 224, 225, 226, 240, 241, 242, 243, 256, 257, 258, 259, 272, 273, 274, 275, 288, 289, 290, 291, 304, 305, 306, 307, 320, 321, 322, 323

Offset

1,1

Comments

Same as A046101 Biquadrateful numbers, until 113 = 81 + 16 + 16. After a finite number of integers which cannot be written as a sum of 4th 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*16 + b*81 + c*625 + d*2401 + e*14641 + ... where a,b,c,d,e,... are nonnegative integers. Sumset of A030514 4th powers of primes.

Mathematica

ok[n_] := {} != Quiet@IntegerPartitions[n, All, Prime[ Range@ PrimePi@ Max[2, n^(1/4)]]^4, 1]; Select[Range[323], ok] (* Giovanni Resta, Jun 12 2016 *)

Crossrefs

Cf. A000040, A030514, A046101.

Sequence in context: A055075 A359831 A048111 * A046101 A360723 A044856

Adjacent sequences: A122611 A122612 A122613 * A122615 A122616 A122617

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 20 2006

Extensions

Several missing terms from Giovanni Resta, Jun 12 2016

Status

approved