A339877 a(n) = A336467(A122111(n)).

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 9, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 9, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 9, 7, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 9, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 7, 1, 3, 9, 1, 1, 3, 1, 1, 9

Offset: 1

Author

Antti Karttunen, Dec 25 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12166
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A064989, A105560, A122111, A336467.

Cf. also A339876, A334108.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
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));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
A339877(n) = A336467(A122111(n));

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A105560(n) = if(1==n,n,prime(bigomega(n)));
A339877(n) = if(1==n||isprime(n),1,A000265(A105560(n)+1) * A339877(A064989(n)));

Formula

For noncomposite n, a(n) = 1, for composite n, a(n) = A000265(A105560(n)+1) * a(A064989(n)).

a(n) = A336467(A122111(n)).