A181812 Range 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

Offset: 1

Author

Matthew Vandermast, Nov 30 2010

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..1000

Programs

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

Formula

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