A340040 - OEIS

%I #11 Sep 12 2021 12:50:33

%S 9,12,28,31,36,43,52,65,68,73,80,89,100,113,126,129,134,141,150,161,

%T 174,189,206,217,220,225,232,241,246,252,265,280,297,316,337,344,347,

%U 352,359,360,368,379,385,392,407,412,424,443,464,487,512,513,516,521,528,537,539

%N Numbers that are the sum of a square s and a cube t such that 0 < s < t.

%e 28 is in the sequence since 1^2 + 3^3 = 1 + 27 = 28, where 0 < 1 < 27.

%t Table[If[Sum[(Floor[i^(1/2)] - Floor[(i - 1)^(1/2)]) (Floor[(n - i)^(1/3)] - Floor[(n - i - 1)^(1/3)]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 700}] // Flatten

%o (Python)

%o from itertools import count, takewhile

%o def aupto(lim):

%o     sqs = list(takewhile(lambda x: x <= lim, (i**2 for i in count(1))))

%o     cbs = list(takewhile(lambda x: x <= lim, (i**3 for i in count(1))))

%o     sms = set(s + t for s in sqs for t in cbs if 0 < s < t and s + t < lim)

%o     return sorted(sms)

%o print(aupto(540)) # _Michael S. Branicky_, Sep 12 2021

%Y Cf. A000290, A000578, A010052, A010057.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Dec 26 2020