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A373767 Integers k such that the sum of the first k noncubes is a square.

%I A373767 #24 Jun 20 2024 11:08:16
%S A373767 3,7,15,37,69,188,254,19274,20798,22380,26439,28219,30057,189067,
%T A373767 279203,369162,1517727,1528134,2964593,3978491,4645227,4701433,
%U A373767 4757977,4895880,4953578,5011614,5062958,7200291,20845013,51370845,101900477,135141272,246185759,358784011,646164289
%N A373767 Integers k such that the sum of the first k noncubes is a square.
%H A373767 Chai Wah Wu, <a href="/A373767/b373767.txt">Table of n, a(n) for n = 1..64</a>
%e A373767 The 3 first noncubes add up to 2+3+4=9, a square. So 3 is a term.
%o A373767 (PARI) nc(n) = n + sqrtnint(n + sqrtnint(n, 3), 3); \\ A007412
%o A373767 snc(n) = sum(k=1, n, nc(k)); \\ A109470
%o A373767 isok(k) = issquare(snc(k));
%o A373767 (Python)
%o A373767 from itertools import count, islice
%o A373767 from sympy.ntheory.primetest import is_square
%o A373767 def A373767_gen(): # generator of terms
%o A373767     k, c = 0, 0
%o A373767     for i in count(1):
%o A373767         for n in range(i**3+1,(i+1)**3):
%o A373767             k += 1
%o A373767             c += n
%o A373767             if is_square(c):
%o A373767                 yield k
%o A373767 A373767_list = list(islice(A373767_gen(),20)) # _Chai Wah Wu_, Jun 18 2024
%Y A373767 Cf. A007412, A109470.
%K A373767 nonn
%O A373767 1,1
%A A373767 _Michel Marcus_, Jun 18 2024
%E A373767 a(14)-a(35) from _Pontus von Brömssen_, Jun 18 2024