A336536 Numbers n that can be written as both the sum of two nonzero fourth powers and the sum of three nonzero fourth powers.

4802, 57122, 76832, 260642, 388962, 617057, 913952, 1229312, 1847042, 1957682, 3001250, 3502322, 3748322, 3959297, 4170272, 4626882, 6223392, 6837602, 6959682, 9872912, 11529602, 14623232, 19668992, 21112002, 27691682, 29552672, 31322912, 31505922, 35701250, 40127377, 40302242, 46712801, 48020000, 48355137

Offset

1,1

Comments

The fourth powers are not necessarily distinct.

If n is in the sequence, then so is k^4*n for every k.

The sum of two nonzero fourth powers is never a fourth power (a case of Fermat's last theorem).

Links

Robert Israel, Table of n, a(n) for n = 1..1072

Example

a(3) = 76832 is in the sequence because 76832 = 14^4 + 14^4 = 6^4 + 10^4 + 16^4.
a(6) = 617057 is in the sequence because 617057 = 7^4 + 28^4 = 3^4 + 20^4 + 26^4.

Maple

N:= 10^8: # for terms <= N
F1:= {seq(i^4, i=1..floor(N^(1/4)))}: n1:= nops(F1):
F2:= select(`<=`, {seq(seq(F1[i]+F1[j], i=1..j), j=1..nops(F1))}, N):
F3:= select(`<=`, {seq(seq(s+t, s=F1), t=F2)}, N):
sort(convert(F3 intersect F2, list));

Prog

(Python)
def aupto(lim):
  p1 = set(i**4 for i in range(1, int(lim**.25)+2) if i**4 <= lim)
  p2 = set(a+b for a in p1 for b in p1 if a+b <= lim)
  p3 = set(apb+c for apb in p2 for c in p1 if apb+c <= lim)
  return sorted(p3 & p2)
print(aupto(5*10**7)) # Michael S. Branicky, Mar 18 2021

Crossrefs

Cf. A000583, A003294, A047714.

Intersection of A003336 and A003337.

Sequence in context: A157628 A214146 A085322 * A035786 A108010 A029553

Adjacent sequences: A336533 A336534 A336535 * A336537 A336538 A336539

Keyword

nonn

Author

Robert Israel, Jul 24 2020

Status

approved