A343970 -id:A343970 - cp's OEIS frontend

A343967 Numbers that are the sum of three positive cubes in five or more ways.

161568, 262683, 314712, 326808, 359568, 443197, 444536, 471960, 503208, 513729, 515376, 526023, 529199, 532683, 552824, 597960, 702729, 736371, 746992, 806688, 844416, 863379, 907479, 924048, 931419, 975213, 1011067, 1028663, 1062937, 1092853, 1152152, 1172016, 1211048, 1232496, 1258011

Offset: 1

David Consiglio, Jr., May 05 2021

nonn

			314712 =  4^3 +  6^3 + 68^3
       =  5^3 + 24^3 + 67^3
       =  6^3 + 30^3 + 66^3
       = 31^3 + 41^3 + 60^3
       = 36^3 + 48^3 + 54^3
so 314712 is a term of this sequence.

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

Cf. A025333, A051167, A343968, A343970, A343987, A344364, A345083.

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 >= 5])
for x in range(len(rets)):
    print(rets[x])

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])

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

Original entry on oeis.org

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])

A344365 Numbers that are the sum of three fourth powers in exactly five ways.

Original entry on oeis.org

1234349298, 1289202642, 1948502738, 2935465442, 4162186322, 5632212978, 7360969778, 8657437698, 8753497298, 11079947522, 15784025138, 17536524642, 19749588768, 20627242272, 21318234098, 31176043808, 35240346162, 37459676898, 39912730578, 42901649042

Offset: 1

Sean A. Irvine, May 15 2021

nonn

			1234349298 is a member of this sequence because 1234349298 = 7^4 + 154^4 + 161^4 = 26^4 + 143^4 + 169^4 = 61^4 + 118^4 + 179^4 = 74^4 + 107^4 + 181^4 = 91^4 + 91^4 + 182^4.

Sean A. Irvine, Table of n, a(n) for n = 1..946

Cf. A343970, A344278, A344357, A344364, A344648.

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, 500)]
for pos in cwr(power_terms, 3):
    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])

A345084 Numbers that are the sum of three third powers in exactly six ways.

Original entry on oeis.org

1296378, 1371735, 1409400, 1614185, 1824040, 1885248, 2101464, 2302028, 2305395, 2542968, 2851848, 2889216, 2974392, 2988441, 3185792, 3380833, 3681280, 3689496, 3706984, 3775680, 3906657, 4109832, 4123008, 4142683, 4422592, 4842872, 4952312, 5005125, 5023656

Offset: 1

David Consiglio, Jr., Jun 07 2021

nonn

Differs from A345083 at term 7 because 2016496 = 5^3 + 71^3 + 117^3 = 9^3 + 65^3 + 119^3 = 18^3 + 20^3 + 125^3 = 46^3 + 96^3 + 99^3 = 53^3 + 59^3 + 117^3 = 65^3 + 89^3 + 99^3 = 82^3 + 84^3 + 93^3.

			1296378 is a term because 1296378 = 3^3 + 75^3 + 94^3  = 8^3 + 32^3 + 107^3  = 20^3 + 76^3 + 93^3  = 30^3 + 58^3 + 101^3  = 32^3 + 80^3 + 89^3  = 59^3 + 74^3 + 86^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A025326, A343970, A344648, A345083, A345085, 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, 1000)]
for pos in cwr(power_terms, 3):
    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])

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A343967 Numbers that are the sum of three positive cubes in five or more ways.

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

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

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A344365 Numbers that are the sum of three fourth powers in exactly five ways.

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A345084 Numbers that are the sum of three third powers in exactly six ways.

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