A345478 - OEIS

%I #10 Jun 22 2022 16:28:34

%S 7,10,13,15,16,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,

%T 37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,

%U 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78

%N Numbers that are the sum of seven squares in one or more ways.

%H Sean A. Irvine, <a href="/A345478/b345478.txt">Table of n, a(n) for n = 1..1000</a>

%e 10 is a term because 10 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2.

%t ssQ[n_]:=Count[IntegerPartitions[n,{7}],_?(AllTrue[Sqrt[#],IntegerQ]&)]>0; Select[ Range[ 80],ssQ] (* _Harvey P. Dale_, Jun 22 2022 *)

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

%o for pos in cwr(power_terms, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v >= 1])

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

%o         print(rets[x])

%Y Cf. A003330, A344805, A345479, A345488.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 19 2021