A051282 2-adic valuation of A025487: largest k such that 2^k divides A025487(n), where A025487 gives products of primorials.

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

Author

Alford Arnold

Keywords

• nice
• nonn

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001055, A002033, A007814, A025487, A045778, A050320, A051903.

Cf. A050322, A050323, A050324, A050325.

Programs

Haskell

a051282 = a007814 . a025487  -- Reinhard Zumkeller, Apr 06 2013

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 *)

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

Formula

a(n) = A007814(A025487(n)) = A051903(A025487(n)). - Matthew Vandermast, Jul 03 2012

Extensions

More terms from Naohiro Nomoto, Mar 11 2001