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A051282
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2-adic valuation of A025487: largest k such that 2^k divides A025487(n), where A025487 gives products of primorials.
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10
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0, 1, 2, 1, 3, 2, 4, 3, 1, 5, 2, 4, 2, 6, 3, 5, 3, 7, 4, 2, 6, 1, 3, 4, 8, 5, 3, 7, 2, 4, 5, 9, 6, 4, 8, 3, 5, 2, 6, 10, 3, 7, 2, 4, 5, 9, 4, 6, 3, 7, 11, 4, 8, 1, 3, 5, 6, 10, 5, 7, 4, 8, 12, 5, 9, 2, 4, 6, 3, 7, 11, 2, 4, 6, 8, 5, 3, 9, 5, 13, 6, 10, 3, 5, 7, 4, 8, 12, 3, 5, 7, 9, 2, 6, 4, 10, 6, 14, 7, 11, 4, 6, 8, 5, 9, 13, 4, 6, 8, 3, 10, 3, 7, 1, 5, 11, 7, 4
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OFFSET
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1,3
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COMMENTS
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a(n) is the number of primorial numbers (A002110) larger than 1 in the representation of A025487(n) as a product of primorial numbers. - Amiram Eldar, Jun 03 2023
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LINKS
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FORMULA
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EXAMPLE
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a(8) = 3 because A025487(8) = 24 and 2^3 divides 24.
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MATHEMATICA
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max = 40000; A025487 = {1}; lpe = {}; Do[ pe = Sort[ FactorInteger[n][[All, 2]]]; If[FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[A025487, n]], {n, 2, max}]; a[n_] := FactorInteger[ A025487[[n]] ][[1, 2]]; a[1] = 0; Table[a[n], {n, 1, Length[A025487]}] (* Jean-François Alcover, Jun 14 2012, after Robert G. Wilson v *)
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PROG
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(Haskell)
(PARI) isA025487(n)=my(k=valuation(n, 2), t); n>>=k; forprime(p=3, default(primelimit), t=valuation(n, p); if(t>k, return(0), k=t); if(k, n/=p^k, return(n==1)))
[valuation(n, 2) | n <- [1..1000], isA025487(n)]
\\ Or, for older versions:
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CROSSREFS
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KEYWORD
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nice,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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