A025363 -id:A025363 - cp's OEIS frontend

A025372 Numbers that are the sum of 4 nonzero squares in 7 or more ways.

130, 135, 138, 148, 150, 154, 162, 170, 172, 175, 178, 180, 182, 183, 186, 187, 189, 190, 195, 196, 198, 199, 202, 207, 210, 213, 214, 215, 217, 218, 220, 222, 223, 225, 226, 228, 229, 230, 231, 234, 235, 237, 238, 242, 243, 244, 245, 246, 247, 250, 252, 253, 255, 258

Offset: 1

David W. Wilson

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares

Cf. A025335, A025363, A025371, A025373, A344800, A345150.

N:= 1000: # for terms <= N
B:= Vector(N):
for i from 1 while 4*i^2 <= N do
  for j from i while i^2 + 3*j^2 <= N do
    for k from j while i^2 + j^2 + 2*k^2 <= N do
      for l from k do
        m:= i^2 + j^2 + k^2 + l^2;
        if m > N then break fi;
        B[m]:= B[m]+1
od od od od:
select(t -> B[t] >= 7, [$1..N]); # Robert Israel, Oct 23 2020

{n: A025428(n) >= 7}. - R. J. Mathar, Jun 15 2018

A345151 Numbers that are the sum of four third powers in exactly seven ways.

Original entry on oeis.org

13104, 18928, 19376, 20755, 21203, 22743, 24544, 24570, 24787, 25172, 25928, 27755, 27846, 28917, 29582, 31031, 31248, 31528, 32858, 34056, 34713, 35289, 35317, 35441, 35497, 35712, 36190, 36288, 36610, 36890, 36946, 38080, 39221, 39440, 39464, 39851, 39942

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345150 at term 6 because 21896 = 1^3 + 11^3 + 19^3 + 22^3 = 2^3 + 2^3 + 12^3 + 26^3 = 2^3 + 3^3 + 19^3 + 23^3 = 2^3 + 5^3 + 15^3 + 25^3 = 3^3 + 10^3 + 16^3 + 24^3 = 3^3 + 17^3 + 19^3 + 19^3 = 4^3 + 6^3 + 20^3 + 22^3 = 5^3 + 8^3 + 14^3 + 25^3 = 7^3 + 11^3 + 17^3 + 23^3 = 8^3 + 9^3 + 19^3 + 22^3.

			13104 is a term 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.

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

Cf. A025363, A344923, A345085, A345149, A345150, A345153, A345181.

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 == 7])
for x in range(len(rets)):
    print(rets[x])

A025382 Numbers that are the sum of 4 distinct nonzero squares in exactly 7 ways.

Original entry on oeis.org

190, 198, 231, 255, 290, 303, 326, 335, 358, 369, 381, 385, 418, 425, 439, 475, 481, 491, 497, 499, 529, 553, 557, 563, 569, 587, 593, 612, 613, 619, 644, 661, 676, 733, 760, 792, 1012, 1132, 1160, 1228, 1252, 1304, 1432, 1672, 2448, 2576, 2704, 3040, 3168, 4048

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025391, A025363.

{n: A025443(n) = 7}. - R. J. Mathar, Jun 15 2018

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A025372 Numbers that are the sum of 4 nonzero squares in 7 or more ways.

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A345151 Numbers that are the sum of four third powers in exactly seven ways.

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A025382 Numbers that are the sum of 4 distinct nonzero squares in exactly 7 ways.

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