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%I #16 Sep 08 2022 08:46:24
%S 1,1,3,4,5,9,7,8,9,25,11,6,13,49,225,128,17,81,19,250,441,121,23,36,
%T 125,169,243,686,29,50625,31,2048,1089,289,1225,216,37,361,1521,2500,
%U 41,194481,43,2662,10125,529,47,13824,343,15625,2601,4394,53,59049,3025
%N a(n) = numerator of Product_{d|n} (d/tau(d)) where tau(k) = the number of divisors of k (A000005).
%C Product_{d|n} (d/tau(d)) >= 1 for all n >= 1.
%H Robert Israel, <a href="/A324506/b324506.txt">Table of n, a(n) for n = 1..10000</a>
%F a(p) = p for p = odd primes.
%e 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, ...
%e 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.
%p f:= proc(n) local d; numer(mul(d/numtheory:-tau(d), d=numtheory:-divisors(n))) end proc:
%p map(f, [$1..100]); # _Robert Israel_, Jan 04 2021
%t Table[Numerator[Product[k/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 60}] (* _G. C. Greubel_, Mar 04 2019 *)
%o (Magma) [Numerator(&*[d / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (Sage) [product(k/sigma(k,0) for k in n.divisors()).numerator() for n in (1..60)] # _G. C. Greubel_, Mar 04 2019
%Y Cf. A000005, A324507 (denominators).
%K nonn,frac
%O 1,3
%A _Jaroslav Krizek_, Mar 03 2019
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