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A338159
The least number which can be represented as a product of the greatest number of distinct positive integers in exactly n ways.
3
1, 12, 60, 96, 360, 576, 480, 15120, 864, 2880, 3360, 6912, 25200, 7680, 20160, 36960, 4320, 93312, 46080, 82944, 221760, 34560, 2494800, 311040, 53760, 88200, 15966720, 30240, 3880800, 1995840, 43200, 322560, 388800, 345600, 970200, 241920, 414720, 5832000, 529200, 5598720
OFFSET
1,2
COMMENTS
k = p_1^2*p_2*...*p_n obviously has exactly n required representations. Hence a(n) exists for any n.
a(n) is the least k such that A338160(k) = n.
All terms are in A025487.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..1283 (first 150 terms from Dmitry Khomovsky)
David A. Corneth, More terms
FORMULA
a(A338160(n)) = n.
A338160(k) <> n for k < a(n).
EXAMPLE
a(60) = 3 because 60 = 2*3*10 = 2*5*6 = 3*4*5 and each number less than 60 does not have exactly 3 such representations (adding the factor 1 to each product doesn't change anything).
CROSSREFS
Cf. A338160.
Sequence in context: A012657 A012406 A097191 * A273691 A094807 A120644
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Oct 14 2020
EXTENSIONS
a(23)-a(40) from Andrew Howroyd, Oct 14 2020
STATUS
approved