cp's OEIS Frontend

A324188 a(n) = A324121(A163511(n)).

%I A324188 #6 Feb 19 2019 00:10:58
%S A324188 1,1,1,2,1,1,12,2,1,4,3,1,4,12,2,2,3,1,24,4,1,2,3,3,12,6,24,4,6,4,8,2,
%T A324188 1,2,3,1,8,24,4,4,3,1,12,6,1,6,3,1,4,120,18,2,24,24,16,4,10,2,48,4,56,
%U A324188 12,4,2,1,1,12,6,1,2,1,1,24,12,48,40,12,8,16,4,1,20,3,3,4,36,6,14,15,3,36,6,21,2,3,3,36,6,720,8,6,4,24,6,120,12
%N A324188 a(n) = A324121(A163511(n)).
%H A324188 Antti Karttunen, <a href="/A324188/b324188.txt">Table of n, a(n) for n = 0..16384</a>
%H A324188 Antti Karttunen, <a href="/A324188/a324188.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%F A324188 a(n) = A324121(A163511(n)) = gcd(A324184(n), A163511(n)*A324183(n)).
%F A324188 For n > 0, a(n) = A324058(A054429(n)).
%o A324188 (PARI)
%o A324188 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A324188 A324121(n) = gcd(sigma(n),n*numdiv(n));
%o A324188 A324188(n) = A324121(A163511(n));
%o A324188 (PARI)
%o A324188 A324183(n) = if(!n,1,n = ((3<<#binary(n\2))-n-1); my(e=0,m=1); while(n>0, if(!(n%2), m *= (1+e); e=0, e++); n >>= 1); (m*(1+e)));
%o A324188 A324184(n) = if(!n,1,my(p=2,mp=p*p,m=1); while(n>1, if(n%2, p=nextprime(1+p); mp = p*p, if((2==n)||!(n%4),mp *= p,m *= (mp-1)/(p-1))); n >>= 1); (m*(mp-1)/(p-1)));
%o A324188 A324188(n) = gcd(A324184(n), A163511(n)*A324183(n));
%Y A324188 Cf. A054429, A324058, A163511, A324121, A324183, A324184, A324187, A324189.
%K A324188 nonn
%O A324188 0,4
%A A324188 _Antti Karttunen_, Feb 17 2019