A025361 -id:A025361 - cp's OEIS frontend

A343986 Numbers that are the sum of four positive cubes in exactly five ways.

5105, 5131, 5616, 5859, 6435, 7777, 9315, 9737, 9793, 10017, 10250, 10458, 10936, 10962, 11000, 11060, 11088, 11592, 11664, 11781, 12168, 12229, 12285, 12320, 12385, 12392, 12707, 13384, 13734, 13832, 13904, 14183, 14239, 14833, 15176, 15596, 15624, 15752, 15759, 15778, 16093, 16289, 16354, 16480, 16569

Offset: 1

David Consiglio, Jr., May 06 2021

nonn

Differs from A343987 at term 6 because 6883 = 2^3 + 2^3 + 2^3 + 19^3 = 2^3 + 5^3 + 15^3 + 15^3 = 3^3 + 8^3 + 8^3 + 18^3 = 4^3 + 11^3 + 14^3 + 14^3 = 5^3 + 11^3 + 11^3 + 16^3 = 8^3 + 9^3 + 9^3 + 17^3.

			5616 is a term because 5616 = 1^3 + 8^3 + 12^3 + 15^3 = 2^3 + 8^3 + 10^3 + 16^3 = 4^3 + 4^3 + 14^3 + 14^3 = 4^3 + 5^3 + 11^3 + 16^3 = 8^3 + 9^3 + 10^3 + 15^3.

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

Cf. A025361, A343970, A343972, A343987, A343988, A344357, A345149.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,50)]
for pos in cwr(power_terms,4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 5])
for x in range(len(rets)):
    print(rets[x])

A025370 Numbers that are the sum of 4 nonzero squares in 5 or more ways.

Original entry on oeis.org

82, 90, 100, 102, 103, 106, 108, 111, 114, 115, 117, 118, 122, 124, 126, 127, 130, 132, 133, 135, 138, 143, 145, 147, 148, 150, 151, 153, 154, 156, 157, 159, 162, 163, 165, 166, 167, 169, 170, 171, 172, 174, 175, 177, 178, 180, 181, 182, 183, 186, 187, 188, 189, 190

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025333, A025361, A025369, A025371, A343987, A344798.

{n: A025428(n) >= 5}. Union of A025371 and A025361. - R. J. Mathar, Jun 15 2018

A025380 Numbers that are the sum of 4 distinct nonzero squares in exactly 5 ways.

Original entry on oeis.org

126, 150, 170, 186, 219, 225, 230, 242, 249, 250, 261, 267, 274, 275, 278, 287, 295, 297, 305, 311, 314, 319, 321, 322, 323, 325, 343, 346, 347, 361, 377, 379, 383, 401, 419, 421, 427, 437, 457, 463, 467, 468, 493, 500, 504, 509, 517, 523, 524, 577, 600, 680, 724, 744

Offset: 1

David W. Wilson

nonn

Robert Israel, Table of n, a(n) for n = 1..114
Index entries for sequences related to sums of squares

Cf. A025389, A025361.

N:= 100000: # for terms <= N
G:= mul(1+x^(i^2)*y, i=1..floor(sqrt(N))):
G4:= series(coeff(G,y,4),x,N+1):
select(t -> coeff(G4,x,t) = 5, [$1..N]): # Robert Israel, Nov 19 2023

{n: A025443(n) = 5}. - R. J. Mathar, Jun 15 2018

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A343986 Numbers that are the sum of four positive cubes in exactly five ways.

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A025370 Numbers that are the sum of 4 nonzero squares in 5 or more ways.

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A025380 Numbers that are the sum of 4 distinct nonzero squares in exactly 5 ways.

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