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.
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
Examples
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.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Programs
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Magma
[Denominator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
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Maple
A323761 := proc(n) denom(A266265(n)/A211776(n)) ; end proc: seq(A323761(n),n=1..20) ; # R. J. Mathar, Feb 13 2019
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PARI
a(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); denominator(p); \\ Michel Marcus, Jan 27 2019
Formula
a(p) = 2 for prime p > 2.
a(n) = 1 for numbers in A323762.
Comments