A345865 -id:A345865 - cp's OEIS frontend

A023051 Numbers that are the sum of two positive cubes in at least four ways (all solutions).

6963472309248, 12625136269928, 21131226514944, 26059452841000, 55707778473984, 74213505639000, 95773976104625, 101001090159424, 159380205560856, 169049812119552, 174396242861568, 188013752349696

Offset: 1

David W. Wilson (revised Oct 15 1997)

nonn

R. K. Guy, Unsolved Problems in Number Theory, D1.

Uwe Hollerbach, Table of n, a(n) for n=1..16939
Uwe Hollerbach, Taxi, Taxi! [Original link, broken]
Uwe Hollerbach, Taxi, Taxi! [Replacement link to Wayback Machine]
Uwe Hollerbach, Taxi! Taxi! [Cached copy from Wayback Machine, html version of top page only]
D. W. Wilson, The Fifth Taxicab Number is 48988659276962496, J. Integer Sequences, Vol. 2, 1999, #99.1.9.

Cf. A001235, A003826, A011541, A018787, A023050, A025295, A051167, A343968, A345865.

b-file extended by Ray Chandler, Jan 19 2009

A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.

Original entry on oeis.org

13896, 40041, 44946, 52200, 53136, 58995, 76168, 82278, 93339, 94184, 105552, 110683, 111168, 112384, 112832, 113400, 143424, 149416, 149904, 167616, 169560, 171296, 175104, 196776, 197569, 208144, 216126, 221696, 222984, 224505, 235808, 240813, 252062, 255312, 262781, 266031, 281728, 291213

Offset: 1

David Consiglio, Jr., May 05 2021

nonn

Differs from A343968 at term 20 because 161568 = 2^3 + 16^3 + 54^3 = 9^3 + 15^3 + 54^3 = 17^3 + 39^3 + 46^3 = 18^3 + 19^3 + 53^3 = 26^3 + 36^3 + 46^3.

			44946 is a term because 44946 = 7^3 + 12^3 + 35^3 = 9^3 + 17^3 + 34^3 = 11^3 + 24^3 + 31^3 = 16^3 + 17^3 + 33^3.

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

Cf. A025324, A025397, A343968, A343970, A343972, A344278, A345865.

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,3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 4])
for x in range(len(rets)):
    print(rets[x])

A344804 Numbers that are the sum of two cubes in exactly three ways.

Original entry on oeis.org

87539319, 119824488, 143604279, 175959000, 327763000, 700314552, 804360375, 958595904, 1148834232, 1407672000, 1840667192, 1915865217, 2363561613, 2622104000, 3080802816, 3235261176, 3499524728, 3623721192, 3877315533, 4750893000, 5544709352, 5602516416

Offset: 1

Sean A. Irvine, Jun 14 2021

nonn

			87539319 is a term because 87539319 = 167^3 + 436^3 = 22^3 + 423^3 = 255^3 + 414^3 (3 representations).
6963472309248 is not a term because 6963472309248 = 2421^3 + 19083^3 = 5436^3 + 18948^3 = 10200^3 + 18072^3 = 13322^3 + 16630^3 (4 representations).  This is the first difference between this sequence and A018787.

Sean A. Irvine, Table of n, a(n) for n = 1..1584

Cf. A018787, A025286, A025397, A343708, A345865.

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A023051 Numbers that are the sum of two positive cubes in at least four ways (all solutions).

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A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.

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A344804 Numbers that are the sum of two cubes in exactly three ways.

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