The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A346328 Numbers that are the sum of eight fifth powers in exactly three ways. 7

%I #6 Jul 31 2021 19:03:45

%S 52417,54518,69634,70954,84458,84489,84700,85481,87582,92233,101264,

%T 102890,112574,117225,119326,134473,143264,143442,143506,149781,

%U 151448,158719,159465,165634,166998,167029,167196,167240,168021,170122,174773,183804,184457

%N Numbers that are the sum of eight fifth powers in exactly three ways.

%C Differs from A345611 at term 105 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.

%H Sean A. Irvine, <a href="/A346328/b346328.txt">Table of n, a(n) for n = 1..10000</a>

%e 52417 is a term because 52417 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5 + 8^5 = 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**5 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 8):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 3])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A345611, A345835, A346280, A346327, A346329, A346338.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jul 13 2021

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 07:52 EDT 2024. Contains 372807 sequences. (Running on oeis4.)