cp's OEIS Frontend

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

%I A244668 #15 Sep 08 2022 08:46:08
%S A244668 1,2,3,8,5,3,7,64,27,50,11,432,13,49,75,1024,17,1944,19,4000,441,121,
%T A244668 23,27648,125,338,729,392,29,11250,31,32768,363,578,1225,10077696,37,
%U A244668 361,1521,256000,41,64827,43,21296,30375,529,47,63700992,343,125000,289,70304,53,354294,3025
%N A244668 Numerators of (product of divisors of n / sum of divisors of n).
%F A244668 Numerators of (A007955(n) / A000203(n)).
%F A244668 a(n) = n if n = 1 or if n is prime.
%F A244668 a(n) < n if and only if n = 6.
%e A244668 a(7) = 7 because the divisors of 7 are 1 and 7, so then (1 * 7) / (1 + 7) = 7 / 8.
%e A244668 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 A244668 a(9) = 27 because the divisors of 9 are 1, 3 and 9, so then (1 * 3 * 9) / (1 + 3 + 9) = 27 / 13.
%t A244668 Table[Numerator[(Times@@Divisors[n])/(Plus@@Divisors[n])], {n, 50}] (* _Alonso del Arte_, Jul 05 2014 *)
%o A244668 (Magma) [Numerator((&*[d: d in Divisors(n)]) / (&+[d: d in Divisors(n)])): n in [1..100]]
%o A244668 (PARI) a007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)) ;
%o A244668 a(n) = numerator(a007955(n)/sigma(n)); \\ _Michel Marcus_, Jul 05 2014
%Y A244668 Cf. A007955, A000203, A145551, A244669, A244670.
%Y A244668 For denominators see A244669.
%K A244668 nonn,frac
%O A244668 1,2
%A A244668 _Jaroslav Krizek_, Jul 04 2014