A346281 -id:A346281 - cp's OEIS frontend

A345826 Numbers that are the sum of seven fourth powers in exactly four ways.

2932, 4147, 4212, 4387, 5427, 5602, 5667, 6627, 6692, 6817, 6822, 6837, 6852, 6867, 7012, 7122, 7251, 7316, 7491, 7747, 7857, 8052, 8097, 8162, 8402, 8467, 8532, 8707, 8787, 9027, 9092, 9157, 9172, 9202, 9237, 9252, 9332, 9412, 9442, 9492, 9572, 9652, 9682

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345570 at term 9 because 6642 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 2^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.

			4147 is a term because 4147 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4.

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

Cf. A345570, A345776, A345816, A345825, A345827, A345836, A346281.

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, 7):
    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])

A345607 Numbers that are the sum of seven fifth powers in four or more ways.

Original entry on oeis.org

893604, 1117071, 1182534, 1414559, 1629244, 1933328, 2280543, 2586035, 2867074, 3050644, 3055295, 3055977, 3256432, 3329360, 3369543, 3436058, 3551890, 3576363, 3896969, 3914877, 3930849, 4055954, 4087746, 4088690, 4093572, 4096665, 4098161, 4104068, 4104310

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			1117071 is a term because 1117071 = 1^5 + 2^5 + 6^5 + 7^5 + 7^5 + 14^5 + 14^5 = 2^5 + 2^5 + 4^5 + 6^5 + 10^5 + 12^5 + 15^5 = 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 7^5 + 16^5 = 3^5 + 5^5 + 6^5 + 6^5 + 7^5 + 8^5 + 16^5.

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

Cf. A345570, A345606, A345608, A345612, A345718, A346281.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    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])

A346280 Numbers that are the sum of seven fifth powers in exactly three ways.

Original entry on oeis.org

84457, 166997, 324860, 326199, 358482, 359327, 391007, 391999, 408158, 455146, 455749, 486468, 502429, 572054, 595519, 614505, 622280, 648319, 671210, 672022, 696468, 696499, 696710, 697491, 699592, 704243, 713274, 729235, 755516, 796467, 857518, 877645

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345606 at term 39 because 893604 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 10^5 + 15^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5.

			84457 is a term because 84457 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5.

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

Cf. A345606, A345825, A346279, A346281, A346328, A346358.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 3])
    for x in range(len(rets)):
        print(rets[x])

A346282 Numbers that are the sum of seven fifth powers in exactly five ways.

Original entry on oeis.org

6768576, 6776120, 7883668, 8625376, 8740709, 10036201, 10604054, 12476826, 12618493, 13006575, 13060213, 13080706, 13174250, 13536416, 13550162, 13662500, 14110656, 15169276, 15247994, 16053313, 16060683, 16374218, 16573507, 16600001, 17735057, 17749152

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345608 at term 16 because 13562501 = 1^5 + 1^5 + 1^5 + 9^5 + 14^5 + 20^5 + 25^5 = 1^5 + 15^5 + 15^5 + 15^5 + 15^5 + 15^5 + 25^5 = 6^5 + 7^5 + 11^5 + 16^5 + 18^5 + 19^5 + 24^5 = 7^5 + 7^5 + 11^5 + 13^5 + 19^5 + 21^5 + 23^5 = 2^5 + 6^5 + 14^5 + 18^5 + 18^5 + 21^5 + 22^5 = 1^5 + 5^5 + 15^5 + 20^5 + 20^5 + 20^5 + 20^5.

			6768576 is a term because 6768576 = 4^5 + 6^5 + 6^5 + 6^5 + 9^5 + 12^5 + 23^5 = 1^5 + 3^5 + 4^5 + 8^5 + 11^5 + 17^5 + 22^5 = 6^5 + 12^5 + 13^5 + 14^5 + 15^5 + 15^5 + 21^5 = 8^5 + 10^5 + 12^5 + 12^5 + 16^5 + 18^5 + 20^5 = 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 18^5 + 20^5.

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

Cf. A345608, A345827, A346281, A346283, A346330, A346360.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    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])

A346329 Numbers that are the sum of eight fifth powers in exactly four ways.

Original entry on oeis.org

391250, 392031, 455750, 519236, 604822, 622281, 672023, 672054, 672265, 673554, 697492, 703978, 707368, 730259, 763292, 857761, 893605, 893636, 893816, 893847, 894027, 894058, 894452, 894628, 896729, 897151, 901380, 903839, 909124, 909597, 910411, 911403

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345612 at term 33 because 926372 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 10^5 + 15^5 = 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 10^5 + 15^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 7^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 6^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5.

			391250 is a term because 391250 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 1^5 + 1^5 + 4^5 + 7^5 + 8^5 + 8^5 + 9^5 + 12^5 = 2^5 + 3^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 3^5 + 3^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5.

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

Cf. A345612, A345836, A346281, A346328, A346330, A346339.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 8):
    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])

A346359 Numbers that are the sum of six fifth powers in exactly four ways.

Original entry on oeis.org

12047994, 20646208, 21017489, 21300963, 21741819, 24993485, 27669050, 28576064, 30193856, 30785920, 35480456, 35735194, 36082750, 37303264, 39035975, 46814942, 47963291, 50047062, 50724345, 52987561, 53076800, 53606848, 55101101, 56766906, 57969327, 58125980

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345718 at term 23 because 54827300 = 4^5 + 7^5 + 21^5 + 22^5 + 23^5 + 33^5 = 5^5 + 10^5 + 15^5 + 20^5 + 28^5 + 32^5 = 1^5 + 14^5 + 16^5 + 19^5 + 28^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 29^5 + 31^5 = 5^5 + 6^5 + 19^5 + 20^5 + 29^5 + 31^5.

			12047994 is a term because 12047994 = 7^5 + 9^5 + 12^5 + 14^5 + 17^5 + 25^5 = 5^5 + 10^5 + 13^5 + 15^5 + 16^5 + 25^5 = 1^5 + 1^5 + 3^5 + 4^5 + 21^5 + 24^5 = 4^5 + 6^5 + 15^5 + 15^5 + 21^5 + 23^5.

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

Cf. A344519, A345718, A345816, A346281, A346358, A346360.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 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 == 4])
    for x in range(len(rets)):
        print(rets[x])

cp's OEIS Frontend

A345826 Numbers that are the sum of seven fourth powers in exactly four ways.

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A345607 Numbers that are the sum of seven fifth powers in four or more ways.

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A346280 Numbers that are the sum of seven fifth powers in exactly three ways.

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A346282 Numbers that are the sum of seven fifth powers in exactly five ways.

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A346329 Numbers that are the sum of eight fifth powers in exactly four ways.

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A346359 Numbers that are the sum of six fifth powers in exactly four ways.

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