A244668 - OEIS

%I #15 Sep 08 2022 08:46:08

%S 1,2,3,8,5,3,7,64,27,50,11,432,13,49,75,1024,17,1944,19,4000,441,121,

%T 23,27648,125,338,729,392,29,11250,31,32768,363,578,1225,10077696,37,

%U 361,1521,256000,41,64827,43,21296,30375,529,47,63700992,343,125000,289,70304,53,354294,3025

%N Numerators of (product of divisors of n / sum of divisors of n).

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

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

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

%e a(7) = 7 because the divisors of 7 are 1 and 7, so then (1 * 7) / (1 + 7) = 7 / 8.

%e 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.

%e a(9) = 27 because the divisors of 9 are 1, 3 and 9, so then (1 * 3 * 9) / (1 + 3 + 9) = 27 / 13.

%t Table[Numerator[(Times@@Divisors[n])/(Plus@@Divisors[n])], {n, 50}] (* _Alonso del Arte_, Jul 05 2014 *)

%o (Magma) [Numerator((&*[d: d in Divisors(n)]) / (&+[d: d in Divisors(n)])): n in [1..100]]

%o (PARI) a007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)) ;

%o a(n) = numerator(a007955(n)/sigma(n)); \\ _Michel Marcus_, Jul 05 2014

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

%Y For denominators see A244669.

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Jul 04 2014