A344941 -id:A344941 - cp's OEIS frontend

A344359 Numbers that are the sum of five fourth powers in exactly five ways.

59779, 67859, 93394, 108274, 112850, 136915, 142354, 151475, 161459, 168979, 181219, 183539, 183604, 185299, 187699, 189394, 193379, 195394, 199090, 199474, 200979, 201874, 202979, 203299, 205859, 211330, 212419, 213730, 217810, 217890, 221779, 223090, 223155, 223714, 226514, 227779, 231235

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

Differs from A344358 at term 8 because 151300 = 3^4 + 3^4 + 3^4 + 12^4 + 19^4 = 3^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 13^4 + 13^4 + 13^4 + 16^4 = 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

			93394 is a term of this sequence because 93394 = 1^4 + 4^4 + 8^4 + 14^4 + 15^4 = 1^4 + 6^4 + 12^4 + 12^4 + 15^4 = 1^4 + 9^4 + 10^4 + 14^4 + 14^4 = 5^4 + 6^4 + 11^4 + 14^4 + 14^4 = 5^4 + 7^4 + 8^4 + 12^4 + 16^4.

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

Cf. A343988, A344355, A344357, A344358, A344941, A345817, A346257.

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, 5):
    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])

A344940 Numbers that are the sum of five fourth powers in six or more ways.

Original entry on oeis.org

151300, 197779, 211059, 217154, 225890, 236194, 236675, 243235, 246674, 250834, 286114, 288579, 300835, 302130, 302210, 303235, 309059, 317795, 320195, 334819, 334899, 335443, 336210, 338914, 346835, 356899, 363379, 366995, 373234, 375619, 389875, 391154

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

			151300 is a term because 151300 = 3^4 + 3^4 + 3^4 + 12^4 + 19^4  = 3^4 + 11^4 + 11^4 + 14^4 + 17^4  = 3^4 + 13^4 + 13^4 + 13^4 + 16^4  = 6^4 + 9^4 + 9^4 + 9^4 + 19^4  = 7^4 + 11^4 + 11^4 + 11^4 + 18^4  = 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

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

Cf. A344358, A344904, A344941, A344942, A345174, A345563, A345864.

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, 5):
    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])

A345818 Numbers that are the sum of six fourth powers in exactly six ways.

Original entry on oeis.org

37811, 38051, 43251, 43571, 44115, 44531, 45155, 45651, 45891, 47411, 47586, 49971, 52195, 53235, 54131, 56290, 57395, 57460, 57570, 59075, 59330, 59860, 60035, 62180, 62211, 63971, 66340, 67026, 67635, 67715, 67860, 67940, 68115, 68291, 68484, 69395, 69410

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345563 at term 1 because 21251 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 12^4 = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4 = 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4 = 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4.

			37811 is a term because 37811 = 1^4 + 2^4 + 2^4 + 7^4 + 11^4 + 12^4 = 2^4 + 2^4 + 4^4 + 7^4 + 9^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 9^4 + 13^4 = 3^4 + 4^4 + 8^4 + 8^4 + 11^4 + 11^4 = 4^4 + 6^4 + 7^4 + 9^4 + 9^4 + 12^4 = 5^4 + 5^4 + 9^4 + 10^4 + 10^4 + 10^4.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A344941, A345563, A345768, A345817, A345819, A345828, A346361.

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, 6):
    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])

A344921 Numbers that are the sum of four fourth powers in exactly six ways.

Original entry on oeis.org

3847554, 5624739, 6044418, 6593538, 6899603, 9851058, 10456338, 11645394, 12378018, 13638738, 16990803, 19081089, 20622338, 20649603, 20755218, 20795763, 24174003, 24368769, 25265553, 25850178, 25899058, 28470339, 29195154, 30295539, 30534018, 30623394

Offset: 1

David Consiglio, Jr., Jun 02 2021

nonn

Differs from A344904 at term 4 because 6576339 = 1^4 + 24^4 + 41^4 + 43^4 = 3^4 + 7^4 + 41^4 + 44^4 = 4^4 + 23^4 + 27^4 + 49^4 = 6^4 + 31^4 + 41^4 + 41^4 = 7^4 + 11^4 + 36^4 + 47^4 = 7^4 + 21^4 + 28^4 + 49^4 = 12^4 + 17^4 + 29^4 + 49^4.

			3847554 is a term 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.

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

Cf. A344357, A344648, A344904, A344923, A344941, A345149.

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

A344943 Numbers that are the sum of five fourth powers in exactly seven ways.

Original entry on oeis.org

197779, 211059, 217154, 236675, 431155, 444019, 480739, 503539, 530659, 548994, 564979, 568450, 571539, 602450, 602770, 621859, 625635, 625939, 626194, 650659, 651954, 653059, 654130, 666739, 687314, 692754, 692899, 698019, 708499, 716739, 728914, 730914

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

Differs from A344942 at term 10 because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4 = 2^4 + 2^4 + 4^4 + 7^4 + 27^4 = 2^4 + 3^4 + 6^4 + 6^4 + 27^4 = 2^4 + 6^4 + 9^4 + 21^4 + 24^4 = 4^4 + 16^4 + 17^4 + 18^4 + 23^4 = 6^4 + 8^4 + 11^4 + 22^4 + 23^4 = 7^4 + 8^4 + 16^4 + 19^4 + 24^4 = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.

			197779 is a term because 197779 = 1^4 + 5^4 + 6^4 + 16^4 + 19^4  = 1^4 + 7^4 + 11^4 + 12^4 + 20^4  = 1^4 + 10^4 + 12^4 + 17^4 + 17^4  = 2^4 + 4^4 + 5^4 + 7^4 + 21^4  = 3^4 + 5^4 + 6^4 + 6^4 + 21^4  = 4^4 + 7^4 + 9^4 + 13^4 + 20^4  = 11^4 + 13^4 + 14^4 + 15^4 + 16^4.

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

Cf. A344923, A344941, A344942, A344945, A345181, A345819.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 7])
for x in range(len(rets)):
    print(rets[x])

A345175 Numbers that are the sum of five third powers in exactly six ways.

Original entry on oeis.org

2430, 2979, 3214, 3249, 3312, 3492, 3520, 3737, 3753, 3788, 3816, 3842, 3942, 3968, 4121, 4185, 4213, 4267, 4355, 4411, 4418, 4446, 4453, 4456, 4465, 4482, 4509, 4563, 4626, 4663, 4670, 4723, 4753, 4896, 4905, 4924, 4938, 4941, 4950, 4960, 4976, 4987, 4994

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

Differs from A345174 at term 20 because 4392 = 1^3 + 1^3 + 10^3 + 10^3 + 11^3 = 1^3 + 2^3 + 2^3 + 9^3 + 14^3 = 1^3 + 8^3 + 9^3 + 10^3 + 10^3 = 2^3 + 2^3 + 3^3 + 5^3 + 15^3 = 2^3 + 3^3 + 5^3 + 8^3 + 14^3 = 2^3 + 8^3 + 8^3 + 8^3 + 12^3 = 3^3 + 6^3 + 7^3 + 8^3 + 13^3 = 5^3 + 5^3 + 5^3 + 9^3 + 13^3.

			2430 is a term because 2430 = 1^3 + 2^3 + 2^3 + 5^3 + 12^3  = 1^3 + 3^3 + 4^3 + 7^3 + 11^3  = 2^3 + 2^3 + 6^3 + 6^3 + 11^3  = 2^3 + 3^3 + 3^3 + 9^3 + 10^3  = 3^3 + 5^3 + 8^3 + 8^3 + 8^3  = 3^3 + 4^3 + 7^3 + 8^3 + 9^3.

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

Cf. A294740, A343988, A344941, A345149, A345174, A345181, A345768.

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

cp's OEIS Frontend

A344359 Numbers that are the sum of five fourth powers in exactly five ways.

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A344940 Numbers that are the sum of five fourth powers in six or more ways.

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A345818 Numbers that are the sum of six fourth powers in exactly six ways.

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A344921 Numbers that are the sum of four fourth powers in exactly six ways.

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A344943 Numbers that are the sum of five fourth powers in exactly seven ways.

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A345175 Numbers that are the sum of five third powers in exactly six ways.

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