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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. 8

%I

%S 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,

%T 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,

%U 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

%N 2-adic valuation of A025487: largest k such that 2^k divides A025487(n), where A025487 gives products of primorials.

%C a(n) can be used for resorting A025487 and sequences indexed by A025487, e.g., A050322, A050323, A050324 and A050325.

%H Reinhard Zumkeller, <a href="/A051282/b051282.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007814(A025487(n)) = A051903(A025487(n)). - _Matthew Vandermast_, Jul 03 2012

%e a(8) = 3 because A025487(8) = 24 and 2^3 divides 24.

%t 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_ *)

%o a051282 = a007814 . a025487 -- _Reinhard Zumkeller_, Apr 06 2013

%o (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)))

%o [valuation(n,2) | n <- [1..1000], isA025487(n)]

%o \\ Or, for older versions:

%o apply(n->valuation(n,2), select(isA025487, [1..1000])) \\ _Charles R Greathouse IV_, Nov 07 2014

%Y A001055, A045778, A002033 and A050320.

%K nice,nonn

%O 1,3

%A _Alford Arnold_

%E More terms from _Naohiro Nomoto_, Mar 11 2001

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Last modified September 21 01:52 EDT 2020. Contains 337266 sequences. (Running on oeis4.)