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return 1 if n==1 else (reduce(mul, [P(i)**f[i] for i in f]))/n

Indranil Ghosh, <a href="/A181812/b181812.txt">Table of n, a(n) for n = 1..1000</a>

(Python)

from sympy import primerange, factorint

from operator import mul

def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])

def a181811(n):

f = factorint(n)

return 1 if n==1 else (reduce(mul, [P(i)**f[i] for i in f]))/n

def a(n): return a181811(2*n - 1) # Indranil Ghosh, May 15 2017

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_Matthew Vandermast (ghodges14(AT)comcast.net), _, Nov 30 2010

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allocated for Matthew VandermastRange of values of A181811, in order of first appearance: a(n) = A181811(2n-1).

1, 2, 6, 30, 4, 210, 2310, 12, 30030, 510510, 60, 9699690, 36, 8, 223092870, 6469693230, 420, 180, 200560490130, 4620, 7420738134810, 304250263527210, 24, 13082761331670030, 900, 60060, 614889782588491410, 1260, 1021020, 32589158477190044730

1,2

a(n)=smallest integer that, upon multiplying any divisor of the n-th odd positive integer (A005408(n)), produces a member of A025487.

A permutation of the members of A025487.

If 2n-1 = Product p(i)^e(i), then a(n) = Product A002110(i-1)^e(i). I.e., a(n)= A181811(A005408(n)).

For any divisor d of 15 (d = 1, 3, 5, 15), 12d (12, 36, 60, 180) is always a member of A025487. 12 is the smallest integer with this relationship to 15; therefore, since 15 = A005408(8), a(8)=12.

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nonn

Matthew Vandermast (ghodges14(AT)comcast.net), Nov 30 2010

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