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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 12:05 EDT 2021. Contains 347586 sequences. (Running on oeis4.)