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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2.

LINKS

Table of n, a(n) for n=1..41.

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

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: A143753 A121164 A086872 * A054792 A144872 A090347

Adjacent sequences:  A323757 A323758 A323759 * A323761 A323762 A323763

KEYWORD

nonn,frac

AUTHOR

Jaroslav Krizek, Jan 26 2019

STATUS

approved

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Last modified June 19 04:44 EDT 2019. Contains 324217 sequences. (Running on oeis4.)