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The prime factorization of a(n) corresponds to the left diagonal of the XOR-triangle built from prime factorization of n, with 2-adic valuation of a(n) given by last row.
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%I #5 May 24 2020 18:33:37

%S 1,2,6,4,30,3,210,8,36,15,2310,24,30030,105,10,16,510510,72,9699690,

%T 120,35,1155,223092870,12,900,15015,216,840,6469693230,5,200560490130,

%U 32,770,255255,21,9,7420738134810,4849845,5005,60,304250263527210,70

%N The prime factorization of a(n) corresponds to the left diagonal of the XOR-triangle built from prime factorization of n, with 2-adic valuation of a(n) given by last row.

%C This sequence is a self-inverse permutation of the natural numbers.

%C This sequence has strong connections with A334727.

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>

%F a(n) = n iff n is a power of 2.

%F a(n^2) = a(n)^2.

%F a(A019565(n)) = A019565(A334727(n)).

%F A006530(a(n)) = A006530(n).

%F A071178(a(n)) = A071178(n).

%e For n = 198:

%e - 198 = 11^1 * 7^0 * 5^0 * 3^2 * 2^1,

%e - the corresponding XOR-triangle is:

%e 1 0 0 2 1

%e 1 0 2 3

%e 1 2 1

%e 3 3

%e 0

%e - so a(n) = 11^1 * 7^1 * 5^1 * 3^3 * 2^0 = 10395.

%o (PARI) a(n) = {

%o my (f=factor(n),

%o m=if (#f~==0, 0, primepi(f[#f~, 1])),

%o x=vector(m, k, valuation(n, prime(m+1-k))),

%o v=1);

%o forstep (i=m, 1, -1,

%o v*=prime(i)^x[1];

%o x=vector(#x-1, k, bitxor(x[k], x[k+1]));

%o );

%o v

%o }

%Y Cf. A006530, A019565, A071178, A334727, A335019.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, May 21 2020