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A136182 a(n) = Product_{k=1..d(n)-1) lcm(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) = the number of positive divisors of n. 4

%I

%S 1,2,3,8,5,72,7,64,27,200,11,20736,13,392,675,1024,17,23328,19,32000,

%T 1323,968,23,23887872,125,1352,729,87808,29,145800000,31,32768,3267,

%U 2312,6125,1451188224,37,2888,4563,204800000,41,74680704,43,340736

%N a(n) = Product_{k=1..d(n)-1) lcm(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) = the number of positive divisors of n.

%C a(n) = the product of the terms in row n of A136181.

%H Diana Mecum and Harvey P. Dale, <a href="/A136182/b136182.txt">Table of n, a(n) for n = 1..10000</a> (Diana Mecum to 516)

%e The positive divisors of 20 are 1,2,4,5,10,20; lcm(1,2)=2, lcm(2,4)=4, lcm(4,5)=20, lcm(5,10)=10, and lcm(10,20)=20, so a(20) = 2*4*20*10*20 = 32000.

%t Table[Times@@(LCM@@@Partition[Divisors[n],2,1]),{n,50}] (* _Harvey P. Dale_, Dec 13 2011 *)

%o (PARI) a(n) = {my(d=divisors(n)); prod(k=1, #d-1, lcm(d[k], d[k+1]));} \\ _Michel Marcus_, Mar 05 2018

%Y Cf. A136179, A136181, A136183.

%K nonn

%O 1,2

%A _Leroy Quet_, Dec 19 2007

%E a(13) onward from _Diana L. Mecum_, Dec 29 2008

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)