A122614 - OEIS

%I #6 Jun 13 2016 08:49:41

%S 16,32,48,64,80,81,96,97,112,113,128,129,144,145,160,161,162,176,177,

%T 178,192,193,194,208,209,210,224,225,226,240,241,242,243,256,257,258,

%U 259,272,273,274,275,288,289,290,291,304,305,306,307,320,321,322,323

%N Sums of 4th powers of primes.

%C 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.

%H Giovanni Resta, <a href="/A122614/b122614.txt">Table of n, a(n) for n = 1..10000</a>

%F 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.

%t 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 *)

%Y Cf. A000040, A030514, A046101.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Sep 20 2006

%E Several missing terms from _Giovanni Resta_, Jun 12 2016