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A296991
Numbers k such that k^2 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.
6
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 21, 24, 27, 32, 36, 40, 42, 48, 54, 64, 72, 81, 84, 96, 108, 120, 128, 135, 144, 162, 168, 189, 192, 216, 243, 256, 270, 280, 288, 324, 336, 360, 378, 384, 432, 448, 486, 512, 540, 576, 640, 648, 672, 729, 756, 768, 828, 840, 864
OFFSET
1,2
COMMENTS
2^k is a term for k >= 0.
LINKS
Eric Weisstein's World of Mathematics, Tau Function
MATHEMATICA
fQ[n_] := Mod[RamanujanTau@n, n^2] == 0; Select[Range@875, fQ] (* Robert G. Wilson v, Dec 23 2017 *)
PROG
(PARI) is(n) = Mod(ramanujantau(n), n^2)==0 \\ Felix Fröhlich, Dec 24 2017
(Python)
from itertools import count, islice
from sympy import divisor_sigma
def A296991_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)*divisor_sigma(m)**2)+sum(i**3*(70*i - 140*n)*divisor_sigma(i)*divisor_sigma(n-i) for i in range(1, m))) % n**2, count(max(startvalue, 1)))
A296991_list = list(islice(A296991_gen(), 20)) # Chai Wah Wu, Nov 08 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 22 2017
STATUS
approved