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

%I A072591 #16 May 31 2025 19:48:28
%S A072591 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 A072591 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 A072591 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 A072591 In prime factorization of n replace multiplication with bitwise logical 'and'.
%C A072591 a(n) = a(A007947(n)); n is prime iff a(n)=n;
%C A072591 a(n)=0 iff n is even and one prime factor is of form 4*k+1.
%H A072591 Paul Tek, <a href="/A072591/b072591.txt">Table of n, a(n) for n = 1..10000</a>
%e A072591 a(35) = a(5*7) = a(5) 'and' a(7) = '101' and '111' = '101' = 5.
%t A072591 a[n_] := BitAnd @@ FactorInteger[n][[All, 1]];
%t A072591 Array[a, 100] (* _Jean-François Alcover_, Nov 16 2021 *)
%o A072591 (Haskell)
%o A072591 import Data.Bits ((.&.))
%o A072591 a072591 = foldl1 (.&.) . a027746_row  -- _Reinhard Zumkeller_, Jul 05 2013
%o A072591 (Python)
%o A072591 from sympy import factorint
%o A072591 from operator import __and__
%o A072591 from functools import reduce
%o A072591 def a(n): return reduce(__and__, (f for f in factorint(n))) if n > 1 else 1
%o A072591 print([a(n) for n in range(1, 95)]) # _Michael S. Branicky_, May 31 2025
%Y A072591 Cf. A072593, A072594, A072592.
%Y A072591 Cf. A027746.
%K A072591 nonn
%O A072591 1,2
%A A072591 _Reinhard Zumkeller_, Jun 23 2002