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A345822 Numbers that are the sum of six fourth powers in exactly ten ways. 7
122915, 151556, 161475, 162755, 173075, 183620, 185315, 199106, 199940, 201875, 202275, 204275, 204340, 204595, 206115, 207395, 209795, 211075, 213731, 217826, 217891, 218515, 221250, 223955, 224180, 225875, 226595, 227186, 228035, 236195, 237796, 237890 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A345567 at term 8 because 197795 = 1^4 + 2^4 + 5^4 + 6^4 + 16^4 + 19^4  = 1^4 + 2^4 + 7^4 + 11^4 + 12^4 + 20^4  = 1^4 + 2^4 + 10^4 + 12^4 + 17^4 + 17^4  = 2^4 + 4^4 + 7^4 + 9^4 + 13^4 + 20^4  = 2^4 + 11^4 + 13^4 + 14^4 + 15^4 + 16^4  = 3^4 + 6^4 + 6^4 + 9^4 + 13^4 + 20^4  = 3^4 + 6^4 + 7^4 + 14^4 + 15^4 + 18^4  = 4^4 + 9^4 + 11^4 + 12^4 + 15^4 + 18^4  = 7^4 + 7^4 + 14^4 + 14^4 + 15^4 + 16^4.

LINKS

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

EXAMPLE

151556 is a term because 151556 = 1^4 + 2^4 + 2^4 + 9^4 + 11^4 + 19^4 = 1^4 + 2^4 + 3^4 + 7^4 + 16^4 + 17^4 = 1^4 + 8^4 + 11^4 + 12^4 + 13^4 + 17^4 = 2^4 + 3^4 + 7^4 + 8^4 + 11^4 + 19^4 = 3^4 + 3^4 + 3^4 + 4^4 + 12^4 + 19^4 = 3^4 + 4^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 4^4 + 13^4 + 13^4 + 13^4 + 16^4 = 4^4 + 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 4^4 + 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 4^4 + 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

PROG

(Python)

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 == 10])

    for x in range(len(rets)):

        print(rets[x])

CROSSREFS

Cf. A341898, A345567, A345772, A345821, A345832, A346365.

Sequence in context: A115545 A224584 A345567 * A254017 A254024 A254891

Adjacent sequences:  A345819 A345820 A345821 * A345823 A345824 A345825

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 26 2021

STATUS

approved

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Last modified October 5 03:25 EDT 2022. Contains 357240 sequences. (Running on oeis4.)