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A323761
Denominator 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, 2, 3, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 16, 15, 2, 1, 2, 9, 16, 2, 2, 1, 6, 2, 8, 9, 2, 8, 2, 45, 16, 2, 16, 1, 2, 2, 16, 9, 2, 8, 2, 9, 32, 2, 2, 25, 6, 9, 16, 9, 2, 1, 16, 9, 16, 2, 2, 1, 2, 2, 32, 315, 16, 8, 2, 9, 16, 8, 2, 1, 2, 2, 32, 9, 16, 8, 2, 9
OFFSET
1,3
COMMENTS
Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2.
LINKS
FORMULA
a(p) = 2 for prime p > 2.
a(n) = 1 for numbers in A323762.
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) = 3.
MAPLE
A323761 := proc(n)
denom(A266265(n)/A211776(n)) ;
end proc:
seq(A323761(n), n=1..20) ; # R. J. Mathar, Feb 13 2019
PROG
(Magma) [Denominator(&*[&*[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); denominator(p); \\ Michel Marcus, Jan 27 2019
CROSSREFS
Cf. A211776, A266265, A323760 (numerator), A323762.
Sequence in context: A209320 A097051 A374451 * A078832 A086410 A185049
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Jan 27 2019
STATUS
approved