cp's OEIS Frontend

A336314 a(n) = A324121(A122111(n)).

%I A336314 #16 Jul 20 2020 02:08:08
%S A336314 1,1,1,2,1,12,1,2,1,4,3,2,1,12,3,2,1,12,1,6,1,4,1,8,4,36,1,10,1,24,3,
%T A336314 2,3,4,24,4,1,12,1,56,1,24,1,2,3,4,1,4,1,6,9,6,1,4,8,8,1,12,9,48,1,4,
%U A336314 1,2,24,120,5,2,3,18,7,12,1,36,2,10,3,24,1,12,3,4,3,112
%N A336314 a(n) = A324121(A122111(n)).
%H A336314 Antti Karttunen, <a href="/A336314/b336314.txt">Table of n, a(n) for n = 1..12000</a>
%H A336314 Antti Karttunen, <a href="/A336314/a336314.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336314 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A336314 a(n) = A324121(A122111(n)) = gcd(A323173(n), A122111(n)*A336315(n)).
%o A336314 (PARI)
%o A336314 A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
%o A336314 A324121(n) = gcd(sigma(n),n*numdiv(n));
%o A336314 A336314(n) = A324121(A122111(n));
%o A336314 (PARI)
%o A336314 \\ Or as a standalone program:
%o A336314 A336314(n) = if(1==n,1,my(f=factor(n),es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,d=1,s=1,x=1,p,e); for(i=1, #es, pri += es[i]; p = prime(pri); e = 1+is[i]-is[1+i]; d *= e; s *= ((p^e)-1)/(p-1); x *= (p^(e-1))); gcd(s,x*d));
%Y A336314 Cf. A122111, A324121, A336315.
%Y A336314 Cf. A336317 (gives the positions where this coincides with A323173).
%Y A336314 Cf. also A335914.
%K A336314 nonn
%O A336314 1,4
%A A336314 _Antti Karttunen_, Jul 19 2020