

A343297


Numbers k such that there are exactly two multisets of cardinality k where the sum equals the product (A033178(k)=2).


1



7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 30, 34, 36, 42, 44, 48, 54, 60, 66, 80, 84, 90, 112, 126, 142, 192, 210, 234, 252, 258, 330, 350, 354, 440, 594, 654, 714, 720, 780, 966, 1102, 2400, 2820, 4350, 4354, 5274, 6174, 6324
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OFFSET

1,1


COMMENTS

At most one of a(n)  1 and 2*a(n)1 are composite. More precisely, a(n) are those positive integers such that exactly one of product(s)*(a(n)+sum(s)k2)+1 can be factored as (product(s)*p1)*(product(s)*q1), where s varies over all multisets of k positive integers and 1 < p <= q < a(n). The first statement is given by considering s = {} and s = {2}. a(50) is greater than 10^4.


LINKS



EXAMPLE

a(5) = 12 because {2,2,2,2,1,1,1,1,1,1,1,1} and {12,2,1,1,1,1,1,1,1,1,1,1} are the only multisets of size 12 where the sum equals the product.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



