A072591 - OEIS

%I #13 Nov 16 2021 07:24:59

%S 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,

%T 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,

%U 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

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

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

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

%H Paul Tek, <a href="/A072591/b072591.txt">Table of n, a(n) for n = 1..10000</a>

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

%t a[n_] := BitAnd @@ FactorInteger[n][[All, 1]];

%t Array[a, 100] (* _Jean-François Alcover_, Nov 16 2021 *)

%o (Haskell)

%o import Data.Bits ((.&.))

%o a072591 = foldl1 (.&.) . a027746_row  -- _Reinhard Zumkeller_, Jul 05 2013

%Y Cf. A072593, A072594, A072592.

%Y Cf. A027746.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 23 2002