A291186 a(n) = numerator of (pod(n) / tau(n)).

1, 1, 3, 8, 5, 9, 7, 16, 9, 25, 11, 288, 13, 49, 225, 1024, 17, 972, 19, 4000, 441, 121, 23, 41472, 125, 169, 729, 10976, 29, 101250, 31, 16384, 1089, 289, 1225, 1119744, 37, 361, 1521, 320000, 41, 388962, 43, 42592, 30375, 529, 47, 127401984, 343, 62500, 2601

Offset: 1

Author

Jaroslav Krizek, Sep 05 2017

Keywords

• nonn
• frac

Comments

pod(n) = the product of the divisors of n (A007955), tau(n) = the number of the divisors of n (A000005).

Examples

			For n = 4; pod(4) / tau(4) = 8 / 3; a(n) = 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A137927 (denominator).

Cf. A000005, A007955, A120736.

Programs

Magma

[Numerator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]): n in [1..1000]];

Maple

f:= proc(n) local D; D:= numtheory:-divisors(n); numer(convert(D,`*`)/nops(D)) end proc:
map(f, [$1..100]); # Robert Israel, Sep 14 2017

Mathematica

Table[Numerator[Apply[Times, Divisors@ n]/DivisorSigma[0, n]], {n, 51}] (* Michael De Vlieger, Sep 05 2017 *)

PARI

a(n) = my(d=divisors(n)); numerator(prod(k=1, #d, d[k])/#d); \\ Michel Marcus, Sep 05 2017

Formula

a(n) = numerator of (A007955(n) / A000005(n)).