login
A244668
Numerators of (product of divisors of n / sum of divisors of n).
2
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
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
For denominators see A244669.
Sequence in context: A084110 A299788 A244915 * A192646 A338841 A100208
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Jul 04 2014
STATUS
approved