A299788 a(n) = denominator of Product_{d|n} (sigma(d)/d) where sigma(k) = the sum of the divisors of k (A000203).
1, 2, 3, 8, 5, 1, 7, 64, 27, 25, 11, 3, 13, 49, 25, 1024, 17, 27, 19, 1000, 441, 121, 23, 16, 125, 169, 729, 7, 29, 625, 31, 32768, 121, 289, 1225, 5832, 37, 361, 1521, 6400, 41, 2401, 43, 1331, 3375, 529, 47, 3072, 343, 31250, 289, 17576, 53, 6561, 3025, 49
Offset: 1
Examples
For n=4; Product_{d|4} (sigma(d)/d) = (sigma(1)/1)*(sigma(2)/2)*(sigma(4)/4) = (1/1)*(3/2)*(7/4) = 21/8; a(4) = 8.
Programs
-
Magma
[Denominator(&*[&+[c: c in Divisors(d)] / d: d in Divisors(n)]): n in [1..100]];
-
Mathematica
Array[Denominator@ Product[DivisorSigma[1, d]/d, {d, Divisors@ #}] &, 51] -
PARI
a(n) = my(p=1); fordiv(n, d, p *= sigma(d)/d); denominator(p); \\ Michel Marcus, Jan 21 2019