The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A345640 Numbers that are the sum of ten fifth powers in eight or more ways. 6

%I #6 Jul 31 2021 15:58:51

%S 944383,953139,953414,985453,1118585,1151438,1185375,1192180,1198879,

%T 1206546,1209912,1216569,1217172,1218912,1223321,1225398,1226654,

%U 1234631,1241834,1242437,1251195,1251406,1252123,1259685,1265563,1265594,1267937,1275375,1281736

%N Numbers that are the sum of ten fifth powers in eight or more ways.

%H Sean A. Irvine, <a href="/A345640/b345640.txt">Table of n, a(n) for n = 1..1000</a>

%e 953139 is a term because 953139 = 1^5 + 1^5 + 1^5 + 3^5 + 8^5 + 10^5 + 10^5 + 10^5 + 12^5 + 13^5 = 1^5 + 2^5 + 2^5 + 6^5 + 6^5 + 8^5 + 9^5 + 9^5 + 12^5 + 14^5 = 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 12^5 + 12^5 + 13^5 = 2^5 + 2^5 + 3^5 + 3^5 + 7^5 + 7^5 + 9^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 11^5 + 11^5 + 12^5 + 13^5 = 2^5 + 3^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 + 15^5 = 3^5 + 3^5 + 3^5 + 4^5 + 4^5 + 6^5 + 10^5 + 10^5 + 13^5 + 13^5 = 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 + 15^5.

%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, 10):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 8])

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

%o print(rets[x])

%Y Cf. A345601, A345625, A345639, A345641, A346353.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 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.

Last modified December 11 11:25 EST 2023. Contains 367724 sequences. (Running on oeis4.)