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A122614 Sums of 4th powers of primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A297288 A055075 A048111 * A046101 A044856 A217558

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

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Last modified December 14 03:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)