A344365 -id:A344365 - cp's OEIS frontend

A344357 Numbers that are the sum of four fourth powers in exactly five ways.

2147874, 2266338, 2690658, 3189603, 3464178, 3754674, 4030419, 4165794, 4457298, 4884114, 5229378, 5978883, 5980178, 5981283, 6014178, 6134994, 6258723, 6313953, 6400194, 6612354, 7088898, 7498323, 7811874, 7918498, 8064018, 8292323, 8630259, 9146034, 9269523, 9388978, 9397683, 9726978

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

Differs from A344356 at term 7 because 3847554 = 2^4 + 13^4 + 29^4 + 42^4 = 2^4 + 21^4 + 22^4 + 43^4 = 6^4 + 11^4 + 17^4 + 44^4 = 6^4 + 31^4 + 32^4 + 37^4 = 9^4 + 29^4 + 32^4 + 38^4 = 13^4 + 26^4 + 32^4 + 39^4.

			2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.

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

Cf. A343986, A344353, A344356, A344359, A344365, A344921.

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, 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])

A343970 Numbers that are the sum of three positive cubes in exactly five ways.

Original entry on oeis.org

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

This sequence differs from A343967 at term 40 because 1296378 = 3^3 + 76^3 + 95^3 = 9^3 + 33^3 + 108^3 = 21^3 + 77^3 + 94^3 = 31^3 + 59^3 + 102^3 = 33^3 + 81^3 + 90^3 = 60^3 + 75^3 + 87^3.

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

Cf. A025325, A343967, A343969, A343986, A344365, A345084.

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])

A344278 Numbers that are the sum of three fourth powers in exactly four ways.

Original entry on oeis.org

5978882, 15916082, 20621042, 22673378, 30623138, 33998258, 39765362, 48432482, 53809938, 61627202, 65413922, 74346818, 84942578, 88258898, 95662112, 103363442, 117259298, 128929682, 131641538, 137149922, 143244738, 155831858, 158811842, 167042642, 174135122, 175706258, 188529362

Offset: 1

David Consiglio, Jr., May 13 2021

nonn

Differs from A344277 at term 37 because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4

			20621042 is a member of this sequence because 20621042 = 5^4 + 54^4 + 59^4 = 10^4 + 51^4 + 61^4 = 25^4 + 46^4 + 63^4 = 26^4 + 39^4 + 65^4

David Consiglio, Jr., Table of n, a(n) for n = 1..7946

Cf. A343969, A344240, A344277, A344353, A344365.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,50)]
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])

A344364 Numbers that are the sum of three fourth powers in five or more ways.

Original entry on oeis.org

292965218, 779888018, 1010431058, 1110995522, 1234349298, 1289202642, 1500533762, 1665914642, 1948502738, 2158376402, 2373191618, 2636686962, 2689817858, 2935465442, 3019732898, 3205282178, 3642994082, 3831800882, 4162186322, 4324686002, 4687443488, 5064808658

Offset: 1

Sean A. Irvine, May 15 2021

nonn

			292965218 is a member of this sequence because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4 (actually has 6 representations, so is a member of this sequence but not of A344365).
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..10000

Cf. A343967, A344277, A344356, A344365, A344647.

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])

A344648 Numbers that are the sum of three fourth powers in exactly six ways.

Original entry on oeis.org

292965218, 1010431058, 1110995522, 1500533762, 1665914642, 2158376402, 2373191618, 2636686962, 2689817858, 3019732898, 3205282178, 3642994082, 3831800882, 4324686002, 4687443488, 5064808658, 5175310322, 6317554418, 6450435362, 6720346178, 7018992162, 7635761042, 7781780258

Offset: 1

David Consiglio, Jr., May 25 2021

nonn

Differs from A344647 at term 2 because 779888018 = 3^4 + 139^4 + 142^4 = 9^4 + 38^4 + 167^4 = 14^4 + 133^4 + 147^4 = 43^4 + 114^4 + 157^4 = 47^4 + 111^4 + 158^4 = 63^4 + 98^4 + 161^4 = 73^4 + 89^4 + 162^4.

			1010431058 is a term because 1010431058 = 13^4 + 143^4 + 156^4 = 31^4 + 132^4 + 163^4 = 44^4 + 123^4 + 167^4 = 52^4 + 117^4 + 169^4 = 69^4 + 103^4 + 172^4 = 81^4 + 92^4 + 173^4.

Sean A. Irvine, Table of n, a(n) for n = 1..5000

Cf. A344365, A344647, A344730, A344921, A345084.

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 == 6])
for x in range(len(rets)):
    print(rets[x])

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A344357 Numbers that are the sum of four fourth powers in exactly five ways.

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A343970 Numbers that are the sum of three positive cubes in exactly five ways.

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A344278 Numbers that are the sum of three fourth powers in exactly four ways.

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A344364 Numbers that are the sum of three fourth powers in five or more ways.

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A344648 Numbers that are the sum of three fourth powers in exactly six ways.

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