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A335049 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.

%I A335049 #5 May 24 2020 18:33:37
%S A335049 1,2,6,4,30,3,210,8,36,15,2310,24,30030,105,10,16,510510,72,9699690,
%T A335049 120,35,1155,223092870,12,900,15015,216,840,6469693230,5,200560490130,
%U A335049 32,770,255255,21,9,7420738134810,4849845,5005,60,304250263527210,70
%N A335049 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 A335049 This sequence is a self-inverse permutation of the natural numbers.
%C A335049 This sequence has strong connections with A334727.
%H A335049 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A335049 <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>
%F A335049 a(n) = n iff n is a power of 2.
%F A335049 a(n^2) = a(n)^2.
%F A335049 a(A019565(n)) = A019565(A334727(n)).
%F A335049 A006530(a(n)) = A006530(n).
%F A335049 A071178(a(n)) = A071178(n).
%e A335049 For n = 198:
%e A335049 - 198 = 11^1 * 7^0 * 5^0 * 3^2 * 2^1,
%e A335049 - the corresponding XOR-triangle is:
%e A335049          1 0 0 2 1
%e A335049           1 0 2 3
%e A335049            1 2 1
%e A335049             3 3
%e A335049              0
%e A335049 - so a(n) = 11^1 * 7^1 * 5^1 * 3^3 * 2^0 = 10395.
%o A335049 (PARI) a(n) = {
%o A335049     my (f=factor(n),
%o A335049         m=if (#f~==0, 0, primepi(f[#f~, 1])),
%o A335049         x=vector(m, k, valuation(n, prime(m+1-k))),
%o A335049         v=1);
%o A335049     forstep (i=m, 1, -1,
%o A335049         v*=prime(i)^x[1];
%o A335049         x=vector(#x-1, k, bitxor(x[k], x[k+1]));
%o A335049     );
%o A335049     v
%o A335049 }
%Y A335049 Cf. A006530, A019565, A071178, A334727, A335019.
%K A335049 nonn,base
%O A335049 1,2
%A A335049 _Rémy Sigrist_, May 21 2020