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A118476
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a(0) = 1; a(n) is least k with n prime factors and k > n*a(n-1).
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1
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1, 2, 6, 20, 81, 408, 2480, 17376, 139040, 1251450, 12514816, 137663064, 1651956992, 21475443200, 300656206080, 4509843098112, 72157489576704, 1226677322842112, 22080191811166208, 419523644412176256, 8390472888243683328, 176199930653117513728
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OFFSET
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0,2
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COMMENTS
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This is a super-polynomial function, as for positive n, a(n) > n!.
Prime factors counted with multiplicity. - Harvey P. Dale, Aug 25 2019
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LINKS
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FORMULA
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a(0) = 1; a(n) least n-almost prime > n*a(n-1).
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EXAMPLE
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a(1) = 2 because 2 is the smallest prime (integer with 1 prime factor) greater than 1 * 1 = 1.
a(2) = 6 because 6 = 2 * 3 is the smallest semiprime (integer with 2 prime factors) greater than 2 * 2 = 4.
a(3) = 20 because 20 = 2^2*5 is the smallest 3-almost prime (integer with 3 prime factors) greater than 3 * 6 = 18.
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MAPLE
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A118476 := proc(n) option remember; local k; if n = 0 then 1; else for k from n*procname(n-1)+1 do if numtheory[bigomega](k) = n then return k; end if; end do: end if; end proc:
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MATHEMATICA
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lkpf[{n_, a_}]:=Module[{k=a(n+1)+1}, While[PrimeOmega[k]!=n+1, k++]; {n+1, k}]; NestList[lkpf, {0, 1}, 21][[All, 2]] (* Harvey P. Dale, Aug 25 2019 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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