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
Examples
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.
Programs
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Magma
[Numerator((&*[d: d in Divisors(n)]) / (&+[d: d in Divisors(n)])): n in [1..100]]
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Mathematica
Table[Numerator[(Times@@Divisors[n])/(Plus@@Divisors[n])], {n, 50}] (* Alonso del Arte, Jul 05 2014 *) -
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