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A072501 Ratio of the product of divisors of n which are > n^(1/2) to product of divisors of n which are < n^(1/2). 3

%I

%S 1,2,3,4,5,9,7,16,9,25,11,48,13,49,25,64,17,162,19,125,49,121,23,576,

%T 25,169,81,343,29,900,31,512,121,289,49,2916,37,361,169,1600,41,2401,

%U 43,1331,405,529,47,12288,49,1250,289,2197,53,6561,121,3136,361,841,59

%N Ratio of the product of divisors of n which are > n^(1/2) to product of divisors of n which are < n^(1/2).

%C It can easily be proved that the ratio is always an integer. a(n) = n if n is a prime or the square of a prime.

%C If 1/3 were chosen as the exponent instead of 1/2, then the sequence would begin: 1, 2, 3, 8, 5, 36, 7, 32, 27, .... If the exponent is decreased along 1/4, 1/5, ..., then the resulting sequence tends towards A007955. - _Michel Marcus_, Sep 17 2013

%H Ivan Neretin, <a href="/A072501/b072501.txt">Table of n, a(n) for n = 1..10000</a>

%e a(20) = 25. The divisors of 20 are 1,2,4,5,10 and 20. a(20) = 10*20/2*4 = 25.

%t Table[Times @@ ((d = Divisors[n])^Sign[d - Sqrt[n]]), {n, 1, 59}] (* _Ivan Neretin_, May 01 2016 *)

%o (PARI) a(n) = {d = divisors(n); pa = 1; pb = 1; fordiv(n, d, if (d^2 < n, pa *= d); if (d^2 > n, pb *= d);); pb/pa;} \\ _Michel Marcus_, Sep 17 2013

%Y Ratio of corresponding terms of A072500 and A072499.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Jul 20 2002

%E More terms from _Sascha Kurz_, Feb 02 2003

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Last modified July 31 17:15 EDT 2021. Contains 346376 sequences. (Running on oeis4.)