A345154 -id:A345154 - cp's OEIS frontend

A345146 Numbers that are the sum of four third powers in nine or more ways.

21896, 36225, 42120, 46683, 46872, 48321, 48825, 50806, 50904, 51408, 51480, 51506, 51688, 52208, 52416, 53200, 53865, 54971, 55575, 56385, 57113, 58338, 58968, 59059, 60480, 60515, 60984, 62244, 62433, 65303, 66024, 66276, 66339, 66430, 67158, 67536, 67851

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			42120 is a term because 42120 = 1^3 + 19^3 + 22^3 + 27^3  = 2^3 + 3^3 + 13^3 + 33^3  = 2^3 + 6^3 + 17^3 + 32^3  = 3^3 + 3^3 + 20^3 + 31^3  = 3^3 + 17^3 + 20^3 + 29^3  = 3^3 + 13^3 + 14^3 + 32^3  = 6^3 + 15^3 + 16^3 + 31^3  = 7^3 + 17^3 + 23^3 + 27^3  = 11^3 + 13^3 + 21^3 + 29^3.

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

Cf. A025374, A344926, A345119, A345152, A345154, A345155, A345185.

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 >= 9])
for x in range(len(rets)):
    print(rets[x])

A344927 Numbers that are the sum of four fourth powers in exactly nine ways.

Original entry on oeis.org

328118259, 385202034, 395613234, 489597858, 625839858, 641398338, 674511618, 693239634, 699598578, 722302434, 779889314, 780278643, 782999714, 791204514, 792005379, 797405714, 797935698, 805299699, 815120658, 822938754, 851527314, 857962914, 870861618

Offset: 1

David Consiglio, Jr., Jun 02 2021

nonn

Differs from A344926 at term 5 because 328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4 = 8^4 + 79^4 + 93^4 + 121^4 = 18^4 + 79^4 + 97^4 + 119^4 = 21^4 + 77^4 + 98^4 + 119^4 = 27^4 + 77^4 + 94^4 + 121^4 = 34^4 + 77^4 + 89^4 + 123^4 = 46^4 + 57^4 + 103^4 + 119^4 = 49^4 + 77^4 + 77^4 + 126^4 = 61^4 + 66^4 + 77^4 + 127^4.

			328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4  = 8^4 + 79^4 + 93^4 + 121^4  = 18^4 + 79^4 + 97^4 + 119^4  = 21^4 + 77^4 + 98^4 + 119^4  = 27^4 + 77^4 + 94^4 + 121^4  = 34^4 + 77^4 + 89^4 + 123^4  = 46^4 + 57^4 + 103^4 + 119^4  = 49^4 + 77^4 + 77^4 + 126^4  = 61^4 + 66^4 + 77^4 + 127^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..64

Cf. A341892, A344751, A344925, A344926, A344929, A345154.

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, 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 == 9])
for x in range(len(rets)):
    print(rets[x])

A345153 Numbers that are the sum of four third powers in exactly eight ways.

Original entry on oeis.org

27720, 30429, 31339, 31402, 33579, 34624, 34776, 36162, 40105, 42695, 44037, 44163, 44226, 44947, 45162, 45675, 46277, 46900, 47600, 49042, 50112, 50689, 51058, 51597, 51805, 52227, 52264, 52507, 53144, 54271, 54873, 55692, 55790, 56240, 58032, 58221, 58312

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345152 at term 1 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.

			30429 is a term because 30429 = 1^3 + 4^3 + 7^3 + 30^3  = 1^3 + 16^3 + 17^3 + 26^3  = 2^3 + 12^3 + 21^3 + 25^3  = 3^3 + 3^3 + 14^3 + 29^3  = 4^3 + 17^3 + 21^3 + 23^3  = 5^3 + 11^3 + 15^3 + 28^3  = 6^3 + 6^3 + 22^3 + 25^3  = 7^3 + 14^3 + 18^3 + 26^3.

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

Cf. A025364, A344925, A345088, A345151, A345152, A345154, A345184.

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 == 8])
for x in range(len(rets)):
    print(rets[x])

A345186 Numbers that are the sum of five third powers in exactly nine ways.

Original entry on oeis.org

6112, 6138, 6462, 6497, 7001, 7038, 7057, 7064, 7099, 7190, 7316, 7328, 7372, 7433, 7561, 7587, 7703, 7759, 7841, 7902, 8163, 8352, 8443, 8560, 8630, 8632, 8928, 8991, 9017, 9136, 9143, 9171, 9288, 9316, 9379, 9505, 9566, 9647, 9658, 9675, 9684, 9745, 9773

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

Differs from A345185 at term 1 because 5860 = 1^3 + 1^3 + 5^3 + 8^3 + 16^3 = 1^3 + 2^3 + 3^3 + 11^3 + 15^3 = 1^3 + 3^3 + 8^3 + 11^3 + 14^3 = 1^3 + 5^3 + 5^3 + 10^3 + 15^3 = 1^3 + 9^3 + 10^3 + 10^3 + 12^3 = 2^3 + 3^3 + 8^3 + 9^3 + 15^3 = 2^3 + 3^3 + 5^3 + 12^3 + 14^3 = 2^3 + 8^3 + 8^3 + 12^3 + 12^3 = 3^3 + 8^3 + 8^3 + 9^3 + 14^3 = 3^3 + 6^3 + 7^3 + 12^3 + 13^3.

			6112 is a term because 6112 = 1^3 + 2^3 + 9^3 + 11^3 + 14^3  = 1^3 + 3^3 + 7^3 + 12^3 + 14^3  = 1^3 + 6^3 + 6^3 + 7^3 + 16^3  = 2^3 + 2^3 + 9^3 + 9^3 + 15^3  = 2^3 + 3^3 + 5^3 + 11^3 + 15^3  = 2^3 + 8^3 + 9^3 + 9^3 + 14^3  = 3^3 + 3^3 + 3^3 + 4^3 + 17^3  = 3^3 + 5^3 + 8^3 + 11^3 + 14^3  = 8^3 + 8^3 + 8^3 + 11^3 + 12^3.

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

Cf. A294743, A341892, A345154, A345184, A345185, A345188, A345771.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 9])
for x in range(len(rets)):
    print(rets[x])

A345120 Numbers that are the sum of three third powers in exactly nine ways.

Original entry on oeis.org

14926248, 16819704, 20168784, 44946000, 45580536, 54042624, 59768064, 62099136, 66203136, 67956624, 69393024, 78008832, 78716448, 79539832, 80621568, 80996544, 89354448, 90757584, 99616392, 100088568, 101352168, 101943360, 112216896, 112720896, 114306984

Offset: 1

David Consiglio, Jr., Jun 08 2021

nonn

Differs from A345119 at term 4 because 34012224 = 35^3 + 215^3 + 287^3 = 38^3 + 152^3 + 311^3 = 40^3 + 113^3 + 318^3 = 44^3 + 245^3 + 266^3 = 71^3 + 113^3 + 317^3 = 99^3 + 191^3 + 295^3 = 101^3 + 226^3 + 276^3 = 117^3 + 185^3 + 295^3 = 161^3 + 215^3 + 269^3 = 172^3 + 213^3 + 266^3.

			14926248 is a term because 14926248 = 2^3 + 33^3 + 245^3  = 11^3 + 185^3 + 203^3  = 14^3 + 32^3 + 245^3  = 50^3 + 113^3 + 236^3  = 71^3 + 89^3 + 239^3  = 74^3 + 189^3 + 196^3  = 89^3 + 185^3 + 197^3  = 98^3 + 148^3 + 219^3  = 105^3 + 149^3 + 217^3.

Sean A. Irvine, Table of n, a(n) for n = 1..6359

Cf. A025329, A344751, A345088, A345119, A345122, A345154.

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 == 9])
for x in range(len(rets)):
    print(rets[x])

A345156 Numbers that are the sum of four third powers in exactly ten ways.

Original entry on oeis.org

21896, 36225, 48825, 51506, 52416, 53200, 58338, 58968, 60480, 66024, 67851, 70434, 70525, 71155, 72819, 76923, 78624, 78912, 85995, 87507, 88641, 90181, 90783, 91728, 93555, 97552, 98280, 98560, 99008, 99225, 99792, 100170, 103040, 104104, 104265, 104958

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345155 at term 3 because 46872 = 1^3 + 16^3 + 22^3 + 30^3 = 2^3 + 11^3 + 17^3 + 33^3 = 3^3 + 3^3 + 4^3 + 35^3 = 3^3 + 4^3 + 26^3 + 29^3 = 3^3 + 5^3 + 23^3 + 31^3 = 4^3 + 10^3 + 24^3 + 30^3 = 5^3 + 17^3 + 23^3 + 29^3 = 6^3 + 10^3 + 20^3 + 32^3 = 11^3 + 11^3 + 21^3 + 31^3 = 11^3 + 14^3 + 17^3 + 32^3 = 19^3 + 21^3 + 21^3 + 25^3.

			21896 is a term 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.

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

Cf. A025366, A344929, A345122, A345154, A345155, A345188.

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 == 10])
for x in range(len(rets)):
    print(rets[x])

cp's OEIS Frontend

A345146 Numbers that are the sum of four third powers in nine or more ways.

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A344927 Numbers that are the sum of four fourth powers in exactly nine ways.

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A345153 Numbers that are the sum of four third powers in exactly eight ways.

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A345186 Numbers that are the sum of five third powers in exactly nine ways.

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A345120 Numbers that are the sum of three third powers in exactly nine ways.

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A345156 Numbers that are the sum of four third powers in exactly ten ways.

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