A345784 - OEIS

%I #6 Jul 31 2021 22:37:08

%S 132,139,158,160,167,174,181,186,193,195,197,200,212,216,219,238,244,

%T 251,258,265,272,277,288,296,298,300,301,303,307,314,315,317,321,322,

%U 327,328,329,333,334,336,338,340,341,348,350,352,356,359,360,361,363,366

%N Numbers that are the sum of eight cubes in exactly two ways.

%C Differs from A345532 at term 16 because 223 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3  = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3  = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3.

%C Likely finite.

%H Sean A. Irvine, <a href="/A345784/b345784.txt">Table of n, a(n) for n = 1..173</a>

%e 139 is a term because 139 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3.

%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, 8):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 2])

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

%o         print(rets[x])

%Y Cf. A345532, A345774, A345783, A345785, A345794, A345834.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021