A355001 - OEIS

%I #9 Jul 18 2022 16:38:43

%S 1,3,1,3,1,5,1,3,5,3,1,5,1,3,5,3,1,5,1,3,5,3,1,5,1,3,5,3,1,7,1,3,1,3,

%T 7,5,1,3,5,3,1,5,1,3,5,3,1,5,1,3,5,3,1,5,7,3,5,3,1,7,1,3,1,3,7,5,1,3,

%U 5,3,1,5,1,3,5,3,1,5,1,3,5,3,1,5,7,3,5,3,1,7,1,3,1,3,7,5,1,3,5,3,1,5,1,3,5

%N Smallest common prime factor of A003961(n) and A276086(n), or 1 if they are coprime, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

%H Antti Karttunen, <a href="/A355001/b355001.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

%F a(n) = A020639(A355442(n)) = A020639(gcd(A003961(n), A276086(n))).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A020639(n) = if(1==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 A355442(n) = gcd(A003961(n), A276086(n));

%o A355001(n) = A020639(A355442(n));

%Y Cf. A003961, A020639, A276086, A284723 (even bisection), A355442, A355820, A355821 (positions of 1's).

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 13 2022