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

1,2

Comments

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A072591, A072594.

Cf. A027746.

Sequence in context: A163457 A285708 A390053 * A394544 A348907 A039635

Adjacent sequences: A072590 A072591 A072592 * A072594 A072595 A072596

Keyword

nonn

Author

Reinhard Zumkeller, Jun 23 2002

Status

approved