VOOZH about

URL: https://oeis.org/A323760

⇱ A323760 - OEIS

login
A323760
Numerator of Product_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k and tau(k) = the number of the divisors of k.
3
1, 1, 3, 8, 5, 27, 7, 128, 27, 125, 11, 10368, 13, 343, 3375, 131072, 17, 118098, 19, 2000000, 9261, 1331, 23, 6879707136, 625, 2197, 19683, 15059072, 29, 38443359375, 31, 2147483648, 35937, 4913, 42875, 101559956668416, 37, 6859, 59319, 10240000000000, 41
OFFSET
1,3
COMMENTS
Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2.
FORMULA
a(p) = p for primes p > 2.
EXAMPLE
For n=4; Product_{d|4} (pod(d)/tau(d)) = (pod(1)/tau(1))*(pod(2)/tau(2))*(pod(4)/tau(4)) = (1/1)*(2/2)*(8/3) = 8/3; a(4) = 8.
MAPLE
A323760 := proc(n)
numer(A266265(n)/A211776(n)) ;
end proc:
seq(A323760(n), n=1..20) ; # R. J. Mathar, Feb 13 2019
MATHEMATICA
A323760[n_] := Numerator[Times @@ Map[Times @@ #/Length[#] &, Divisors[Rest[Divisors[n]]]]];
Array[A323760, 50] (* Paolo Xausa, Sep 11 2025 *)
PROG
(Magma) [Numerator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]];
(PARI) a(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); numerator(p); \\ Michel Marcus, Jan 27 2019
CROSSREFS
Cf. A211776, A266265, A323761 (denominator).
Sequence in context: A086872 A389125 A363421 * A054792 A144872 A090347
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Jan 26 2019
STATUS
approved