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

1, 2, 4, 6, 8, 16, 24, 32, 64, 96, 128, 256, 288, 384, 512, 1024, 1536, 2048, 4096, 6144, 8192, 16384, 18432, 24576, 32768, 65536, 98304, 131072, 172032, 262144, 276480, 393216, 524288, 1048576, 1179648, 1572864, 1935360, 2097152, 2621440, 3538944, 4194304

Offset: 1

Author

Seiichi Manyama, Dec 22 2017

Keywords

• nonn

Comments

2^k is a term for k >= 0.

Links

• Eric Weisstein's World of Mathematics, Tau Function.

Crossrefs

Cf. A000594, A063938, A296991, A296992.

Programs

Python

from itertools import count, islice
from sympy import divisor_sigma
def A296993_gen(startvalue=1): # generator of terms >= startvalue
    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)))
A296993_list = list(islice(A296993_gen(),10)) # Chai Wah Wu, Nov 08 2022