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.

1, 2, 3, 8, 5, 72, 7, 64, 27, 200, 11, 20736, 13, 392, 675, 1024, 17, 23328, 19, 32000, 1323, 968, 23, 23887872, 125, 1352, 729, 87808, 29, 145800000, 31, 32768, 3267, 2312, 6125, 1451188224, 37, 2888, 4563, 204800000, 41, 74680704, 43, 340736

Offset

1,2

Comments

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

Links

Diana Mecum and Harvey P. Dale, Table of n, a(n) for n = 1..10000 (Diana Mecum to 516)

Example

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.

Mathematica

Table[Times@@(LCM@@@Partition[Divisors[n], 2, 1]), {n, 50}] (* Harvey P. Dale, Dec 13 2011 *)

Prog

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

Crossrefs

Cf. A136179, A136181, A136183.

Sequence in context: A109844 A128779 A112283 * A170911 A067911 A243103

Adjacent sequences: A136179 A136180 A136181 * A136183 A136184 A136185

Keyword

nonn

Author

Leroy Quet, Dec 19 2007

Extensions

a(13) onward from Diana L. Mecum, Dec 29 2008

Status

approved