A345122 - OEIS

%I #7 Jul 31 2021 23:41:49

%S 34012224,58995000,71319312,72505152,92853216,94118760,95331816,

%T 139755888,147545280,150506000,157464000,159874560,161023680,

%U 164186352,171904032,182393856,184909824,188224128,189771336,191260224,199108125,201342240,202440384,217054720

%N Numbers that are the sum of three third powers in exactly ten ways.

%C Differs from A345121 at term 3 because 69190848 = 23^3 + 107^3 + 407^3  = 23^3 + 191^3 + 395^3  = 33^3 + 271^3 + 365^3  = 35^3 + 299^3 + 347^3  = 50^3 + 137^3 + 404^3  = 89^3 + 308^3 + 338^3  = 95^3 + 178^3 + 396^3  = 107^3 + 179^3 + 395^3  = 121^3 + 149^3 + 399^3  = 152^3 + 254^3 + 365^3  = 206^3 + 215^3 + 368^3.

%H Sean A. Irvine, <a href="/A345122/b345122.txt">Table of n, a(n) for n = 1..2238</a>

%e 34012224 is a term because 34012224 = 35^3 + 215^3 + 287^3  = 38^3 + 152^3 + 311^3  = 40^3 + 113^3 + 318^3  = 44^3 + 245^3 + 266^3  = 71^3 + 113^3 + 317^3  = 99^3 + 191^3 + 295^3  = 101^3 + 226^3 + 276^3  = 117^3 + 185^3 + 295^3  = 161^3 + 215^3 + 269^3  = 172^3 + 213^3 + 266^3.

%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**3 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 3):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 10])

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

%o     print(rets[x])

%Y Cf. A025330, A344861, A345120, A345121, A345156.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 08 2021

%E More terms from _Sean A. Irvine_, Jun 08 2021