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A338112
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Least number that is both the sum and product of n distinct positive integers.
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1
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1, 3, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000
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OFFSET
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1,2
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COMMENTS
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Each a(n) = n! except that a(2) = 1+2 = 3. For n > 0, only each integer >= A000217(n) is the sum of n distinct positive integers. For the integers that are products of these types, see below.
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LINKS
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FORMULA
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a(n) = A000142(n) for n = 1 and n > 2; a(2) = 3.
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EXAMPLE
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a(1) = 1 because we define sums and products as sum(m) := prod(m) := m for all integers m in this case where these normally-binary operations only have one operand.
a(3) = 6 because 6 = 1+2+3 = 1*2*3 (with all the distinct positive integers the same in the sum and the product only for this term and a(1)).
a(5) = 120 because 120 = 1+2+3+4+110 (= ... = 22+23+24+25+26) = 1*2*3*4*5.
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MATHEMATICA
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With[{nn=30}, Rest[CoefficientList[Series[x (2+x-x^2)/(2(1-x)), {x, 0, nn}], x] Range[0, nn]!]] (* Harvey P. Dale, Aug 10 2021 *)
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PROG
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(PARI) a(n) = if(n<1, , if(n==2, 3, n!))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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