A296991 Numbers k such that k^2 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.
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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..500
- Eric Weisstein's World of Mathematics, Tau Function
Programs
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Mathematica
fQ[n_] := Mod[RamanujanTau@n, n^2] == 0; Select[Range@875, fQ] (* Robert G. Wilson v, Dec 23 2017 *)
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PARI
is(n) = Mod(ramanujantau(n), n^2)==0 \\ Felix Fröhlich, Dec 24 2017
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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
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