

A063938


Numbers n such that n divides tau(n), where tau(n)=A000594(n) is Ramanujan's tau function.


16



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
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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

Seiichi Manyama, Table of n, a(n) for n = 1..10000
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 2.8) 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


CROSSREFS

For the sequence when n is prime see A007659.
Cf. A063940, A000594, A079334, A296991, A296993.
Sequence in context: A056757 A225737 A079333 * A002473 A174995 A161466
Adjacent sequences: A063935 A063936 A063937 * A063939 A063940 A063941


KEYWORD

nonn,easy


AUTHOR

Robert G. Wilson v, Aug 31 2001


EXTENSIONS

More terms from Dean Hickerson, Jan 03 2003


STATUS

approved



