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A182856
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a(0) = 1; for n > 0, a(n) = smallest positive integer whose prime signature contains, for k = 1 to n, exactly one positive number appearing exactly k times.
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2
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OFFSET
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0,2
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COMMENTS
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Next term has 105 digits.
Smallest number k with A323022(k) = n, where A323022(m) is the number of distinct multiplicities in the prime signature of m. - Gus Wiseman, Jan 03 2019
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LINKS
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FORMULA
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EXAMPLE
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The canonical prime factorization of a(3) = 1801800 is 2^3*3^2*5^2*7*11*13. The prime signature of 1801800 is therefore (3,2,2,1,1,1). Note that (3,2,2,1,1,1) contains exactly one number that appears once (3), one number that appears twice (2), and one number that appears three times (1).
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MATHEMATICA
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Table[Product[Times@@Prime[i*(i-1)/2+Ceiling[Range[i*(n-i)]/(n-i)]], {i, n-1}], {n, 6}] (* Gus Wiseman, Jan 03 2019 *)
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PROG
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(PARI) a(n) = if(n == 0, return(1)); my(f = matrix(binomial(n+1, 2), 2)); f[, 1] = primes(#f~ )~; f[, 2] = Vecrev(concat(vector(n, i, vector(n+1-i, j, i))))~; factorback(f) \\ David A. Corneth, Jan 03 2019
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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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