A344189 Numbers that are the sum of four fourth powers in exactly one way.

4, 19, 34, 49, 64, 84, 99, 114, 129, 164, 179, 194, 244, 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, 1218, 1252, 1267, 1282, 1299, 1314, 1329, 1332, 1344, 1347, 1379, 1393

Offset

1,1

Comments

Differs from A003338 at term 14 because 259 = 1^4 + 1^4 + 1^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Example

34 is a member of this sequence because 34 = 1^4 + 1^4 + 2^4 + 2^4

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 50)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A003338, A025403, A344188, A344190, A344193, A344642.

Sequence in context: A282506 A047715 A003338 * A031291 A210374 A352116

Adjacent sequences: A344186 A344187 A344188 * A344190 A344191 A344192

Keyword

nonn

Author

David Consiglio, Jr., May 11 2021

Status

approved