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A072594
In prime factorization of n replace multiplication with bitwise logical 'xor'.
11
1, 2, 3, 0, 5, 1, 7, 2, 0, 7, 11, 3, 13, 5, 6, 0, 17, 2, 19, 5, 4, 9, 23, 1, 0, 15, 3, 7, 29, 4, 31, 2, 8, 19, 2, 0, 37, 17, 14, 7, 41, 6, 43, 11, 5, 21, 47, 3, 0, 2, 18, 13, 53, 1, 14, 5, 16, 31, 59, 6, 61, 29, 7, 0, 8, 10, 67, 17, 20, 0, 71, 2, 73, 39, 3, 19, 12, 12, 79, 5, 0, 43, 83, 4
OFFSET
1,2
COMMENTS
n is prime iff a(n)=n;
for primes p, k>0: a(p^k)=p*(k mod 2);
for m>1: a(m^2)=0, see A072595.
a(A127812(n)) = n and a(m) <> n for m < A127812(n).
LINKS
EXAMPLE
a(35) = a(5*7) = a(5) 'xor' a(7) = '101' xor '111' = '010' = 2.
MATHEMATICA
a[n_] := BitXor @@ Flatten[ Table[ First[#], {Last[#]} ]& /@ FactorInteger[n] ]; Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Mar 11 2013 *)
PROG
(Haskell)
import Data.Bits (xor)
a072594 = foldl1 xor . a027746_row :: Integer -> Integer
-- Reinhard Zumkeller, Nov 17 2012
(PARI) a(n)=if(n==1, return(1)); my(f=factor(n), t); for(i=1, #f~, if(f[i, 2]%2, t=bitxor(t, f[i, 1]))); t \\ Charles R Greathouse IV, Aug 28 2016
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Reinhard Zumkeller, Jun 23 2002
STATUS
approved