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A296993 Numbers k such that k^3 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

%I A296993 #18 Feb 16 2025 08:33:52
%S A296993 1,2,4,6,8,16,24,32,64,96,128,256,288,384,512,1024,1536,2048,4096,
%T A296993 6144,8192,16384,18432,24576,32768,65536,98304,131072,172032,262144,
%U A296993 276480,393216,524288,1048576,1179648,1572864,1935360,2097152,2621440,3538944,4194304
%N A296993 Numbers k such that k^3 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.
%C A296993 2^k is a term for k >= 0.
%H A296993 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TauFunction.html">Tau Function.</a>
%o A296993 (Python)
%o A296993 from itertools import count, islice
%o A296993 from sympy import divisor_sigma
%o A296993 def A296993_gen(startvalue=1): # generator of terms >= startvalue
%o A296993     return filter(lambda n: not -24*((m:=n+1>>1)**2*(0 if n&1 else (m*(35*m - 52*n) + 18*n**2)*divisor_sigma(m)**2)+sum((i*(i*(i*(70*i - 140*n) + 90*n**2)))*divisor_sigma(i)*divisor_sigma(n-i) for i in range(1,m))) % n**3, count(max(startvalue,1)))
%o A296993 A296993_list = list(islice(A296993_gen(),10)) # _Chai Wah Wu_, Nov 08 2022
%Y A296993 Cf. A000594, A063938, A296991, A296992.
%K A296993 nonn
%O A296993 1,2
%A A296993 _Seiichi Manyama_, Dec 22 2017