A331283 - OEIS

%I #12 Jan 14 2020 22:18:56

%S 1,2,1,1,1,6,1,4,9,2,1,4,1,2,3,1,1,6,1,4,3,2,1,2,1,2,1,4,1,6,1,2,3,2,

%T 1,3,1,2,3,20,1,6,1,4,1,2,1,12,1,2,3,4,1,2,1,8,3,2,1,30,1,2,1,1,1,6,1,

%U 4,3,2,1,18,1,2,3,4,1,6,1,8,1,2,1,12,1,2,3,8,1,10,1,4,3,2,1,2,1,2,1,5,1,6,1,8,3

%N a(n) = gcd(n, A329605(n)), where A329605(n) gives the number of divisors of primorial inflation of n, A108951(n).

%H Antti Karttunen, <a href="/A331283/b331283.txt">Table of n, a(n) for n = 1..11025</a>

%H Antti Karttunen, <a href="/A331283/a331283.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

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

%F a(n) = gcd(n, A329605(n)).

%F a(A002110(n)) = gcd(A002110(n), A000142(1+n)) = A034386(1+n), for n >= 0.

%o (PARI) A331283(n) = if(1==n,1,my(f=factor(n),e=1,m=1); forstep(i=#f~,1,-1, e += f[i,2]; m *= e^(primepi(f[i,1])-if(1==i,0,primepi(f[i-1,1])))); gcd(n,m));

%Y Cf. A000142, A002110, A034386, A108951, A329605.

%Y Cf. also A009191, A329612.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 14 2020