A072591 In prime factorization of n replace multiplication with bitwise logical 'and'.

1, 2, 3, 2, 5, 2, 7, 2, 3, 0, 11, 2, 13, 2, 1, 2, 17, 2, 19, 0, 3, 2, 23, 2, 5, 0, 3, 2, 29, 0, 31, 2, 3, 0, 5, 2, 37, 2, 1, 0, 41, 2, 43, 2, 1, 2, 47, 2, 7, 0, 1, 0, 53, 2, 1, 2, 3, 0, 59, 0, 61, 2, 3, 2, 5, 2, 67, 0, 3, 0, 71, 2, 73, 0, 1, 2, 3, 0, 79, 0, 3, 0, 83, 2, 1, 2, 1, 2, 89, 0, 5, 2, 3, 2

Offset

1,2

Comments

a(n) = a(A007947(n)); n is prime iff a(n)=n;

a(n)=0 iff n is even and one prime factor is of form 4*k+1.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Example

a(35) = a(5*7) = a(5) 'and' a(7) = '101' and '111' = '101' = 5.

Mathematica

a[n_] := BitAnd @@ FactorInteger[n][[All, 1]];
Array[a, 100] (* Jean-François Alcover, Nov 16 2021 *)

Prog

(Haskell)
import Data.Bits ((.&.))
a072591 = foldl1 (.&.) . a027746_row  -- Reinhard Zumkeller, Jul 05 2013

Crossrefs

Cf. A072593, A072594, A072592.

Cf. A027746.

Sequence in context: A318057 A136096 A284694 * A085308 A209190 A086286

Adjacent sequences: A072588 A072589 A072590 * A072592 A072593 A072594

Keyword

nonn

Author

Reinhard Zumkeller, Jun 23 2002

Status

approved