A079334 -id:A079334 - cp's OEIS frontend

A063938 Numbers k that divide tau(k), where tau(k)=A000594(k) is Ramanujan's tau function.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 88, 90, 91, 92, 96, 98, 100, 105, 108, 112, 115, 120, 125, 126, 128, 135, 140, 144, 147, 150, 160, 161, 162, 168

Offset: 1

Robert G. Wilson v, Aug 31 2001

Although most small numbers are in the sequence, it becomes sparser for larger values; e.g., only 504 numbers up to 10000 and only 184 numbers from 10001 to 20000 are in the sequence.

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Tau Function.

For the sequence when n is prime see A007659.

Cf. A063940, A000594, A079334, A296991, A296993.

(* First do <Michael De Vlieger, Dec 23 2017 *)

for (n=1,1000,if(Mod(ramanujantau(n),n)==0,print1(n", "))) \\ Dana Jacobsen, Sep 06 2015

use ntheory ":all"; my @p = grep { !(ramanujan_tau($) % $) } 1..1000; say "@p"; # Dana Jacobsen, Sep 06 2015

from itertools import count, islice
from sympy import divisor_sigma
def A063938_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: not -840*(pow(m:=n+1>>1,2,n)*(0 if n&1 else pow(m*divisor_sigma(m),2,n))+(sum(pow(i,4,n)*divisor_sigma(i)*divisor_sigma(n-i) for i in range(1,m))<<1)) % n, count(max(startvalue,1)))
A063938_list = list(islice(A063938_gen(),25)) # Chai Wah Wu, Nov 08 2022

More terms from Dean Hickerson, Jan 03 2003

A299157 Numbers k such that k+1 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

Original entry on oeis.org

2, 3, 5, 6, 7, 11, 13, 17, 19, 20, 22, 23, 27, 29, 31, 41, 45, 47, 53, 55, 59, 68, 71, 76, 77, 79, 83, 87, 89, 91, 97, 104, 107, 114, 127, 137, 139, 149, 160, 167, 171, 177, 179, 183, 191, 195, 199, 209, 223, 229, 239, 240, 243, 251, 269, 275, 293, 297, 321, 343

Offset: 1

Seiichi Manyama, Feb 04 2018

nonn

Numbers k such that A299163(k) = 0.

Seiichi Manyama, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Tau Function.

Cf. A000594, A063938, A079334, A296991, A299158, A299163.

q[k_] := Divisible[RamanujanTau[k], k+1]; Select[Range[350], q] (* Amiram Eldar, Jan 08 2025 *)

isok(n) = (ramanujantau(n) % (n+1)) == 0; \\ Michel Marcus, Feb 05 2018

cp's OEIS Frontend

A063938 Numbers k that divide tau(k), where tau(k)=A000594(k) is Ramanujan's tau function.

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