cp's OEIS Frontend

A334990 a(1) = 1 and for any n > 1 with prime factorization Product_{k = 1..m} prime(k)^e_k (where prime(k) denotes the k-th prime number and e_m > 0), a(n) = Product_{k = 1..m-1} prime(k)^(e_k XOR e_{k+1}) (where XOR denotes the bitwise XOR operator).

%I A334990 #6 May 24 2020 18:33:23
%S A334990 1,1,2,1,3,1,5,1,4,6,7,8,11,10,2,1,13,8,17,12,30,14,19,4,9,22,8,20,23,
%T A334990 1,29,1,42,26,3,1,31,34,66,24,37,15,41,28,108,38,43,32,25,18,78,44,47,
%U A334990 4,105,40,102,46,53,8,59,58,180,1,165,21,61,52,114,6
%N A334990 a(1) = 1 and for any n > 1 with prime factorization Product_{k = 1..m} prime(k)^e_k (where prime(k) denotes the k-th prime number and e_m > 0), a(n) = Product_{k = 1..m-1} prime(k)^(e_k XOR e_{k+1}) (where XOR denotes the bitwise XOR operator).
%C A334990 This sequence has similarities with A038554; here we consider prime exponents, there binary digits.
%H A334990 <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>
%F A334990 a(n) = 1 iff n belongs to A100778.
%F A334990 a(n^2) = a(n)^2.
%F A334990 a(n^k) = a(n)^k for any k >= 0 and any squarefree number n.
%F A334990 a(prime(n+1)) = prime(n).
%F A334990 A006530(a(n)) < A006530(n) for any n > 1.
%o A334990 (PARI) a(n) = { my (v=1, p=2, e=valuation(n,p)); n/=p^e; forprime (q=p+1, oo, if (n==1, return (v), my (f=valuation(n,q)); n/=q^f; v*=p^bitxor(e,f); [p,e]=[q,f])) }
%Y A334990 Cf. A006530, A038554, A100778.
%K A334990 nonn,base
%O A334990 1,3
%A A334990 _Rémy Sigrist_, May 18 2020