A342666 a(n) = A336466(A156552(n)).

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 1, 9, 1, 5, 1, 11, 1, 3, 3, 3, 1, 3, 1, 15, 1, 21, 1, 1, 1, 1, 5, 3, 1, 9, 1, 33, 5, 9, 1, 23, 1, 1, 3, 65, 1, 7, 1, 35, 21, 5, 1, 21, 1, 341, 9, 3, 1, 11, 1, 27, 1, 5, 1, 5, 1, 15, 3, 51, 1, 27, 1, 39, 1, 1365, 1, 1, 5, 49, 9, 1, 1, 1, 1, 117, 5, 825, 3, 9, 1, 9, 3, 1, 1, 7, 1

Offset: 2

Author

Antti Karttunen, Mar 18 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A003961, A156552, A322993, A336466.

Cf. also A324104, A342651, A342656, A350067.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
A342666(n) = A336466(A156552(n));

PARI

\\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt
v156552sigs = readvec("a156552.txt");
A000265(n) = (n>>valuation(n,2));
A342666(n) = if(isprime(n),1,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); prod(i=1,#ps,A000265(ps[i]-1)^es[i])); \\ Antti Karttunen, Jan 29 2022

Formula

a(n) = A336466(A156552(n)) = A336466(A322993(n)).

a(p) = 1 for all primes p.

a(A003961(n)) = a(n).