A345607 -id:A345607 - cp's OEIS frontend

A345570 Numbers that are the sum of seven fourth powers in four or more ways.

2932, 4147, 4212, 4387, 5427, 5602, 5667, 6627, 6642, 6692, 6707, 6772, 6817, 6822, 6837, 6852, 6867, 6882, 6947, 7012, 7122, 7251, 7316, 7491, 7747, 7857, 7922, 7987, 8052, 8097, 8162, 8227, 8402, 8467, 8532, 8707, 8787, 8962, 9027, 9092, 9157, 9172, 9202

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			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. A345522, A345561, A345569, A345571, A345579, A345607, A345826.

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])

A345606 Numbers that are the sum of seven fifth powers in three or more 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., Jun 20 2021

nonn

			166997 is a term because 166997 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 = 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 10^5 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 10^5.

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

Cf. A345569, A345604, A345605, A345607, A345611, A346280.

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])

A345608 Numbers that are the sum of seven fifth powers in five or more ways.

Original entry on oeis.org

6768576, 6776120, 7883668, 8625376, 8740709, 10036201, 10604054, 12476826, 12618493, 13006575, 13060213, 13080706, 13174250, 13536416, 13550162, 13562501, 13662500, 14110656, 14583968, 15169276, 15247994, 16053313, 16060683, 16374218, 16573507, 16600001

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6776120 is a term because 6776120 = 2^5 + 4^5 + 7^5 + 12^5 + 17^5 + 18^5 + 20^5 = 3^5 + 6^5 + 6^5 + 12^5 + 14^5 + 18^5 + 21^5 = 4^5 + 6^5 + 8^5 + 11^5 + 13^5 + 16^5 + 22^5 = 4^5 + 7^5 + 7^5 + 7^5 + 16^5 + 19^5 + 20^5 = 5^5 + 6^5 + 6^5 + 8^5 + 16^5 + 19^5 + 20^5.

Sean A. Irvine, Table of n, a(n) for n = 1..4721

Cf. A345571, A345607, A345609, A345613, A345719, A346282.

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])

A345612 Numbers that are the sum of eight fifth powers in four or more 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., Jun 20 2021

nonn

			392031 is a term because 392031 = 1^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 2^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5.

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

Cf. A345579, A345607, A345611, A345613, A345621, A346329.

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])

A345718 Numbers that are the sum of six fifth powers in four or more 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, 54827300, 55101101, 56766906

Offset: 1

David Consiglio, Jr., Jun 24 2021

nonn

			20646208 is a term because 20646208 = 2^5 + 12^5 + 12^5 + 16^5 + 18^5 + 28^5 = 3^5 + 4^5 + 4^5 + 8^5 + 10^5 + 29^5 = 6^5 + 6^5 + 12^5 + 14^5 + 24^5 + 26^5 = 7^5 + 7^5 + 8^5 + 16^5 + 25^5 + 25^5.

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

Cf. A344518, A345561, A345604, A345607, A345719, A346359.

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])

A346281 Numbers that are the sum of seven fifth powers in exactly four 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., Jul 13 2021

nonn

Differs from A345607 at term 92 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.

			893604 is a term 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.

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

Cf. A345607, A345826, A346280, A346282, A346329, A346359.

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])

cp's OEIS Frontend

A345570 Numbers that are the sum of seven fourth powers in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345606 Numbers that are the sum of seven fifth powers in three or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345608 Numbers that are the sum of seven fifth powers in five or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345612 Numbers that are the sum of eight fifth powers in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345718 Numbers that are the sum of six fifth powers in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A346281 Numbers that are the sum of seven fifth powers in exactly four ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python