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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A072591, A072594.

Cf. A027746.

Programs

Haskell

import Data.Bits (((.|.))
a072593 = foldl1 (.|.) . a027746_row  -- Reinhard Zumkeller, Jul 05 2013

Mathematica

Array[BitOr @@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &, 120] (* Michael De Vlieger, May 31 2025 *)

PARI

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

Python

from sympy import factorint
from operator import _or_
from functools import reduce
def a(n): return reduce(_or_, (f for f in factorint(n))) if n > 1 else 1
print([a(n) for n in range(1, 84)]) # Michael S. Branicky, May 31 2025