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

1,2

Comments

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

Links

Seiichi Manyama, Table of n, a(n) for n = 1..500

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

Cf. A000594, A063938, A296992, A296993.

Sequence in context: A279542 A053640 A344470 * A097755 A301704 A083854

Adjacent sequences: A296988 A296989 A296990 * A296992 A296993 A296994

Keyword

nonn

Author

Seiichi Manyama, Dec 22 2017

Status

approved