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A324506 a(n) = numerator of Product_{d|n} (d/tau(d)) where tau(k) = the number of divisors of k (A000005). 2
1, 1, 3, 4, 5, 9, 7, 8, 9, 25, 11, 6, 13, 49, 225, 128, 17, 81, 19, 250, 441, 121, 23, 36, 125, 169, 243, 686, 29, 50625, 31, 2048, 1089, 289, 1225, 216, 37, 361, 1521, 2500, 41, 194481, 43, 2662, 10125, 529, 47, 13824, 343, 15625, 2601, 4394, 53, 59049, 3025 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(p) = p for p = odd primes.

EXAMPLE

Product_{d|n} (d/tau(d)) for n >= 1: 1, 1, 3/2, 4/3, 5/2, 9/4, 7/2, 8/3, 9/2, 25/4, 11/2, 6, 13/2, 49/4, 225/16, ...

For n=4; Product_{d|4} (d/tau(d)) = (1/tau(1)) * (2/tau(2)) * (4/tau(4)) = (1/1) * (2/2) * (4/3) = 4/3; a(4) = 4.

MATHEMATICA

Table[Numerator[Product[k/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 60}] (* G. C. Greubel, Mar 04 2019 *)

PROG

(MAGMA) [Numerator(&*[d / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]

(Sage) [product(k/sigma(k, 0) for k in n.divisors()).numerator() for n in (1..60)] # G. C. Greubel, Mar 04 2019

CROSSREFS

Cf. A000005, A324507 (denominators).

Sequence in context: A122403 A302653 A300738 * A065336 A079097 A202475

Adjacent sequences:  A324503 A324504 A324505 * A324507 A324508 A324509

KEYWORD

nonn,frac

AUTHOR

Jaroslav Krizek, Mar 03 2019

STATUS

approved

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)