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A072593 In prime factorization of n replace multiplication with bitwise logical 'or'.

%I A072593 #17 May 31 2025 19:48:49
%S A072593 1,2,3,2,5,3,7,2,3,7,11,3,13,7,7,2,17,3,19,7,7,11,23,3,5,15,3,7,29,7,
%T A072593 31,2,11,19,7,3,37,19,15,7,41,7,43,11,7,23,47,3,7,7,19,15,53,3,15,7,
%U A072593 19,31,59,7,61,31,7,2,13,11,67,19,23,7,71,3,73,39,7,19,15,15,79,7,3,43,83
%N A072593 In prime factorization of n replace multiplication with bitwise logical 'or'.
%C A072593 a(n) = a(A007947(n)); n is prime iff a(n)=n.
%H A072593 Paul Tek, <a href="/A072593/b072593.txt">Table of n, a(n) for n = 1..10000</a>
%e A072593 a(35) = a(5*7) = a(5) 'or' a(7) = '101' or '111' = '111' = 7.
%t A072593 Array[BitOr @@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &, 120] (* _Michael De Vlieger_, May 31 2025 *)
%o A072593 (Haskell)
%o A072593 import Data.Bits (((.|.))
%o A072593 a072593 = foldl1 (.|.) . a027746_row  -- _Reinhard Zumkeller_, Jul 05 2013
%o A072593 (PARI)
%o A072593 a072593(n) = if(n<2, return(1)); my(F=factor(n), v=Vec(F[,1]), x=v[1]); for(k=2, #v, x=bitor(x,v[k])); x \\ _Hugo Pfoertner_, May 31 2025
%o A072593 (Python)
%o A072593 from sympy import factorint
%o A072593 from operator import __or__
%o A072593 from functools import reduce
%o A072593 def a(n): return reduce(__or__, (f for f in factorint(n))) if n > 1 else 1
%o A072593 print([a(n) for n in range(1, 84)]) # _Michael S. Branicky_, May 31 2025
%Y A072593 Cf. A072591, A072594.
%Y A072593 Cf. A027746.
%K A072593 nonn
%O A072593 1,2
%A A072593 _Reinhard Zumkeller_, Jun 23 2002