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A063938
Numbers k that divide tau(k), where tau(k)=A000594(k) is Ramanujan's tau function.
17
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
1,2
COMMENTS
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.
LINKS
Eric Weisstein's World of Mathematics, Tau Function.
MATHEMATICA
(* First do <<NumberTheory`Ramanujan` *) test[n_] := Mod[RamanujanTau[n], n]==0; Select[Range[200], test]
(* Second program: *)
Select[Range@ 168, Divisible[RamanujanTau@ #, #] &] (* Michael De Vlieger, Dec 23 2017 *)
PROG
(PARI) for (n=1, 1000, if(Mod(ramanujantau(n), n)==0, print1(n", "))) \\ Dana Jacobsen, Sep 06 2015
(Perl) use ntheory ":all"; my @p = grep { !(ramanujan_tau($_) % $_) } 1..1000; say "@p"; # Dana Jacobsen, Sep 06 2015
(Python)
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
CROSSREFS
For the sequence when n is prime see A007659.
Sequence in context: A225737 A357315 A079333 * A002473 A174995 A161466
KEYWORD
nonn,easy
AUTHOR
Robert G. Wilson v, Aug 31 2001
EXTENSIONS
More terms from Dean Hickerson, Jan 03 2003
STATUS
approved