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A072594
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In prime factorization of n replace multiplication with bitwise logical 'xor'.
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11
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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
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OFFSET
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1,2
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COMMENTS
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n is prime iff a(n)=n;
for primes p, k>0: a(p^k)=p*(k mod 2);
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LINKS
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EXAMPLE
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a(35) = a(5*7) = a(5) 'xor' a(7) = '101' xor '111' = '010' = 2.
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MATHEMATICA
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a[n_] := BitXor @@ Flatten[ Table[ First[#], {Last[#]} ]& /@ FactorInteger[n] ]; Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Mar 11 2013 *)
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PROG
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(Haskell)
import Data.Bits (xor)
a072594 = foldl1 xor . a027746_row :: Integer -> Integer
(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
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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