A047715 Numbers that are the sum of 4 but no fewer nonzero fourth powers.

4, 19, 34, 49, 64, 84, 99, 114, 129, 164, 179, 194, 244, 259, 274, 289, 304, 324, 339, 354, 369, 419, 434, 499, 514, 529, 544, 594, 609, 628, 643, 658, 673, 674, 708, 723, 738, 769, 784, 788, 803, 849, 868, 883, 898, 913, 963, 978, 1024, 1043, 1138, 1153

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn

Comments

First differs from A003338 at term 64: A003338(64) = 1393 is also a term of A003337, so not a term here. - Michael S. Branicky, Apr 19 2021

Crossrefs

Cf. A000583, A002377, A003338 (sum of 4), A003337 (sum of 3), A003336 (sum of 2), A344188, A344187.

Programs

Python

limit = 1153
from functools import lru_cache
qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 3 <= limit]
qds = set(qd)
@lru_cache(maxsize=None)
def findsums(n, m):
  if m == 1: return {(n,)} if n in qds else set()
  return set(tuple(sorted(t+(q,))) for q in qds for t in findsums(n-q, m-1))
A003338s = set(n for n in range(4, limit+1) if len(findsums(n, 4)) >= 1)
A003337s = set(n for n in range(3, limit+1) if len(findsums(n, 3)) >= 1)
A003336s = set(n for n in range(2, limit+1) if len(findsums(n, 2)) >= 1)
print(sorted(A003338s - A003337s - A003336s - qds)) # Michael S. Branicky, Apr 19 2021

Formula

Equals A003338 - A344188 - A344187 - A000583, where "-" denotes "set difference". - Sean A. Irvine, May 15 2021