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A226532 If n = Product_{i>0} prime(i)^e(i), then a(n) = Product_{i>0} prime(i)^(XOR_{j>=i} e(j)), where XOR is bitwise XOR.

%I A226532 #22 Jan 01 2025 22:12:01
%S A226532 1,2,6,4,30,3,210,8,36,15,2310,24,30030,105,5,16,510510,72,9699690,
%T A226532 120,35,1155,223092870,12,900,15015,216,840,6469693230,10,
%U A226532 200560490130,32,385,255255,7,9,7420738134810,4849845,5005,60,304250263527210,70,13082761331670030,9240,1080,111546435,614889782588491410
%N A226532 If n = Product_{i>0} prime(i)^e(i), then a(n) = Product_{i>0} prime(i)^(XOR_{j>=i} e(j)), where XOR is bitwise XOR.
%C A226532 This sequence is a permutation of the natural numbers.
%C A226532 The powers of 2 are the fixed points of this sequence.
%C A226532 a(prime(i)) = A002110(i) for any i > 0.
%C A226532 a(i^2) = a(i)^2 for any i > 0.
%C A226532 a(A019565(n)) = A019565(A006068(n)) for any n >= 0.
%H A226532 Paul Tek, <a href="/A226532/b226532.txt">Table of n, a(n) for n = 1..2370</a>
%H A226532 Paul Tek, <a href="/A226532/a226532.txt">PERL program for this sequence</a>
%H A226532 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A226532 a(50) = a(2^1 * 3^0 * 5^2)
%e A226532       = 2^xor(1,0,2) * 3^xor(0,2) * 5^xor(2)
%e A226532       = 2^3          * 3^2        * 5^2
%e A226532       = 1800.
%o A226532 (Perl) # See Tek link.
%o A226532 (Haskell)
%o A226532 import Data.Bits (xor)
%o A226532 a226532 n = product $ zipWith (^)
%o A226532             a000040_list (scanr1 xor $ a067255_row n :: [Integer])
%o A226532 -- _Reinhard Zumkeller_, Jun 11 2013
%Y A226532 Cf. A006068.
%Y A226532 Cf. A226569 (inverse), A067255, A000040.
%K A226532 nonn
%O A226532 1,2
%A A226532 _Paul Tek_, Jun 10 2013