A244668 Numerators of (product of divisors of n / sum of divisors of n).

1, 2, 3, 8, 5, 3, 7, 64, 27, 50, 11, 432, 13, 49, 75, 1024, 17, 1944, 19, 4000, 441, 121, 23, 27648, 125, 338, 729, 392, 29, 11250, 31, 32768, 363, 578, 1225, 10077696, 37, 361, 1521, 256000, 41, 64827, 43, 21296, 30375, 529, 47, 63700992, 343, 125000, 289, 70304, 53, 354294, 3025

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

Numerators of (A007955(n) / A000203(n)).

a(n) = n if n = 1 or if n is prime.

a(n) < n if and only if n = 6.

Example

a(7) = 7 because the divisors of 7 are 1 and 7, so then (1 * 7) / (1 + 7) = 7 / 8.
a(8) = 64 because the divisors of 8 are 1, 2, 4 and 8, so then (1 * 2 * 4 * 8) / (1 + 2 + 4 + 8) = 64 / 15.
a(9) = 27 because the divisors of 9 are 1, 3 and 9, so then (1 * 3 * 9) / (1 + 3 + 9) = 27 / 13.

Mathematica

Table[Numerator[(Times@@Divisors[n])/(Plus@@Divisors[n])], {n, 50}] (* Alonso del Arte, Jul 05 2014 *)

Prog

(Magma) [Numerator((&*[d: d in Divisors(n)]) / (&+[d: d in Divisors(n)])): n in [1..100]]
(PARI) a007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)) ;
a(n) = numerator(a007955(n)/sigma(n)); \\ Michel Marcus, Jul 05 2014

Crossrefs

Cf. A007955, A000203, A145551, A244669, A244670.

For denominators see A244669.

Sequence in context: A084110 A299788 A244915 * A192646 A338841 A100208

Adjacent sequences: A244665 A244666 A244667 * A244669 A244670 A244671

Keyword

nonn,frac

Author

Jaroslav Krizek, Jul 04 2014

Status

approved