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%I #10 Nov 18 2019 16:42:57
%S 0,1,0,2,1,3,0,3,0,2,1,2,0,3,1,4,1,1,0,3,0,2,1,5,2,3,0,2,0,0,1,5,1,2,
%T 3,6,0,3,0,4,1,1,0,3,1,2,1,4,0,3,1,2,0,7,2,5,0,3,1,7,0,2,0,6,3,0,1,3,
%U 1,2,0,7,1,3,2,2,1,1,0,5,0,2,1,6,2,3,0,4,0,6,0,3,1,2,3,7,1,1,1,4,0,0,1,5,3
%N Bitwise-XOR of exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).
%C Positions of records are: 1, 2, 4, 6, 16, 24, 36, 54, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 65536, ..., conjectured also to be the positions of the first occurrence of each n.
%H Antti Karttunen, <a href="/A329647/b329647.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(n) = A268387(A108951(n)).
%F a(n) <= A329616(n).
%o (PARI)
%o A034386(n) = prod(i=1, primepi(n), prime(i));
%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A268387(n) = if(n>1, fold(bitxor, factor(n)[, 2]), 0);
%o A329647(n) = A268387(A108951(n));
%Y Cf. A034386, A108951, A268387, A329615, A329616.
%K nonn
%O 1,4
%A _Antti Karttunen_, Nov 18 2019
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