

A132181


a(n)=smallest positive integer such that product{k=1 to n}(1+1/a(k)) has a prime numerator.


1



1, 2, 6, 1, 28, 1, 1, 58, 1, 708, 1, 1, 2, 1, 2836, 1, 1, 22696, 1, 1, 1, 590122, 1, 12, 1, 1, 2, 1, 1180246, 1, 9441976, 1, 1, 1, 169955586, 1, 2, 1, 2, 1, 2719289392, 1, 1, 1, 1, 5438578786, 1, 32631472722, 1, 2, 1, 391577672676, 1, 1, 2, 1, 1566310690708, 1, 1
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OFFSET

1,2


LINKS

Owen Whitby, Table of n, a(n) for n = 1..200


FORMULA

Comments from Owen Whitby, May 07 2008 (Start): Successive terms a(.) can be calculated using the following recurrences for the numerator n(.) and denominator d(.) of the product.
a(1)=1; n(1)=1, d(1)=1 ==> a(2)=1, n(2)=2, d(2)=1 ( to start things off );
n(i)=2, d(i)= odd ==> a(i+1)=q1, n(i+1)=q, d(i+1)=d(i)(q1)/2 where q is least odd prime not dividing d(i);
n(i)=odd prime, d(i)=1 ==> a(i+1)=c*n(i), n(i+1)=c*n(i)+1, d(i+1)=c where c is least even integer such that c*n(i)+1 is prime;
n(i)=odd prime, d(i)=even ==> a(i+1)=1, n(i+1)=n(i), d(i+1)=d(i)/2;
n(i)=odd prime, d(i)= odd>=3 ==> a(i+1)=p1, n(i+1)=n(i), d(i+1)=d(i)(p1)/p where p is least prime divisor of d(i). (End)


CROSSREFS

Sequence in context: A281521 A281635 A180512 * A291646 A027642 A249306
Adjacent sequences: A132178 A132179 A132180 * A132182 A132183 A132184


KEYWORD

nonn


AUTHOR

Leroy Quet, Nov 04 2007


EXTENSIONS

a(10) to a(59) and list of 200 terms added by Owen Whitby, May 07 2008


STATUS

approved



