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

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, 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, 1, 2, 24, 120, 5, 2, 3, 18, 7, 12, 1, 36, 2, 10, 3, 24, 1, 12, 3, 4, 3, 112

Offset: 1

Author

Antti Karttunen, Jul 19 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A122111, A324121, A336315.

Cf. A336317 (gives the positions where this coincides with A323173).

Cf. also A335914.

Programs

PARI

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));
A324121(n) = gcd(sigma(n),n*numdiv(n));
A336314(n) = A324121(A122111(n));

PARI

\\ Or as a standalone program:
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));

Formula

a(n) = A324121(A122111(n)) = gcd(A323173(n), A122111(n)*A336315(n)).