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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 (list; graph; refs; listen; history; text; internal format)
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)-k-2)+1 can be factored as (product(s)*p-1)*(product(s)*q-1), 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
Michael W. Ecker, When Does a Sum of Positive Integers Equal Their Product?, Mathematics Magazine 75(1), 2002, pp. 41-47.
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
Sequence in context: A236683 A120200 A356635 * A106108 A120309 A035705
KEYWORD
nonn
AUTHOR
Nathaniel Gregg, Apr 11 2021
STATUS
approved

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Last modified April 12 22:36 EDT 2024. Contains 371639 sequences. (Running on oeis4.)