A353517 - OEIS

%I #11 Apr 25 2022 08:11:10

%S 1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,1,3,1,

%T 1,3,1,1,3,1,1,3,1,1,3,1,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,1,3,1,1,3,1,1,

%U 3,1,1,3,1,1,3,1,3,1,3,3,1,3,3,1,3,3,1,3,3,1,3,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1

%N The largest proper divisor of A276086(2*n) reduced modulo 4, where A276086(n) the primorial base exp-function.

%H Antti Karttunen, <a href="/A353517/b353517.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A353516(2*n) = A010873(A324895(2*n)).

%F For n >= 1, a(n) = (A353487(n) * A353527(n)) mod 4.

%F For n >= 1, a(n) = A353487(n-1). [See A353516 for a proof]

%o (PARI)

%o A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A324895(n) = A032742(A276086(n));

%o A353517(n) = (A324895(2*n)%4);

%Y Even bisection of A353516. Sequence A353487 shifted one term right.

%Y Cf. A010873, A032742, A276086, A324895, A353527.

%K nonn

%O 0,3

%A _Antti Karttunen_, Apr 24 2022