A025362 -id:A025362 - cp's OEIS frontend

A025371 Numbers that are the sum of 4 nonzero squares in 6 or more ways.

90, 124, 130, 133, 135, 138, 147, 148, 150, 154, 156, 157, 159, 162, 163, 165, 166, 170, 171, 172, 174, 175, 177, 178, 180, 182, 183, 186, 187, 188, 189, 190, 193, 195, 196, 198, 199, 201, 202, 203, 205, 207, 210, 213, 214, 215, 217, 218, 219, 220, 222, 223, 225, 226

Offset: 1

David W. Wilson

nonn

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares

Cf. A025334, A025362, A025370, A025372, A344799, A345148.

limit = 226
from functools import lru_cache
sq = [k**2 for k in range(1, int(limit**.5)+2) if k**2 + 3 <= limit]
sqs = set(sq)
@lru_cache(maxsize=None)
def findsums(n, m):
  if m == 1: return {(n, )} if n in sqs else set()
  return set(tuple(sorted(t+(s,))) for s in sqs for t in findsums(n-s, m-1))
print([n for n in range(4, limit+1) if len(findsums(n, 4)) >= 6]) # Michael S. Branicky, Apr 20 2021

{n: A025428(n) >= 6}. Union of A025372 and A025362. - R. J. Mathar, Jun 15 2018

A345149 Numbers that are the sum of four third powers in exactly six ways.

Original entry on oeis.org

6883, 12411, 13923, 14112, 14581, 14896, 14904, 15561, 15876, 16317, 16640, 17208, 17479, 17992, 18739, 18865, 19035, 19080, 19665, 19712, 19763, 19880, 20007, 20384, 20979, 21231, 21420, 21707, 22409, 22617, 23149, 23940, 24355, 25515, 25984, 26208, 26334

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345148 at term 3 because 13104 = 1^3 + 10^3 + 16^3 + 18^3 = 1^3 + 11^3 + 14^3 + 19^3 = 2^3 + 9^3 + 15^3 + 19^3 = 4^3 + 6^3 + 14^3 + 20^3 = 4^3 + 9^3 + 10^3 + 21^3 = 5^3 + 7^3 + 11^3 + 21^3 = 8^3 + 9^3 + 14^3 + 19^3.

			6883 is a term because 6883 = 2^3 + 2^3 + 2^3 + 18^3  = 2^3 + 4^3 + 14^3 + 14^3  = 3^3 + 7^3 + 7^3 + 17^3  = 3^3 + 10^3 + 13^3 + 13^3  = 4^3 + 10^3 + 10^3 + 15^3  = 7^3 + 8^3 + 8^3 + 16^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A025362, A343986, A344921, A345084, A345148, A345151, A345175.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 6])
for x in range(len(rets)):
    print(rets[x])

A025381 Numbers that are the sum of 4 distinct nonzero squares in exactly 6 ways.

Original entry on oeis.org

174, 234, 254, 258, 266, 273, 279, 285, 291, 309, 327, 333, 339, 359, 362, 365, 371, 380, 391, 395, 396, 403, 413, 443, 444, 449, 451, 476, 487, 492, 521, 572, 596, 604, 643, 668, 692, 696, 772, 796, 936, 1016, 1032, 1064, 1448, 1520, 1584, 1776, 1904, 1968, 2288

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025390, A025362.

{n: A025443(n) = 6}. - R. J. Mathar, Jun 15 2018

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A025371 Numbers that are the sum of 4 nonzero squares in 6 or more ways.

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A345149 Numbers that are the sum of four third powers in exactly six ways.

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Programs

Python

A025381 Numbers that are the sum of 4 distinct nonzero squares in exactly 6 ways.

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Author

Keywords

Links

Crossrefs

Formula