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A051282
2-adic valuation of A025487: largest k such that 2^k divides A025487(n), where A025487 gives products of primorials.
10
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
OFFSET
1,3
COMMENTS
a(n) can be used for resorting A025487 and sequences indexed by A025487, e.g., A050322, A050323, A050324 and A050325.
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
LINKS
FORMULA
a(n) = A007814(A025487(n)) = A051903(A025487(n)). - Matthew Vandermast, Jul 03 2012
EXAMPLE
a(8) = 3 because A025487(8) = 24 and 2^3 divides 24.
MATHEMATICA
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 *)
PROG
(Haskell)
a051282 = a007814 . a025487 -- Reinhard Zumkeller, Apr 06 2013
(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:
apply(n->valuation(n, 2), select(isA025487, [1..1000])) \\ Charles R Greathouse IV, Nov 07 2014
KEYWORD
nice,nonn
AUTHOR
EXTENSIONS
More terms from Naohiro Nomoto, Mar 11 2001
STATUS
approved