A342651 a(n) = A329697(A156552(n)).

0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 3, 2, 3, 0, 3, 1, 3, 2, 3, 0, 3, 0, 3, 1, 5, 1, 3, 0, 1, 3, 3, 0, 3, 0, 4, 2, 6, 0, 4, 1, 2, 3, 4, 0, 3, 2, 4, 5, 4, 0, 4, 0, 7, 3, 4, 1, 4, 0, 5, 1, 2, 0, 3, 0, 4, 2, 4, 1, 5, 0, 4, 2, 8, 0, 3, 3, 7, 6, 4, 0, 3, 2, 6, 4, 9, 3, 4, 0, 4, 3, 2, 0, 5, 0, 5, 3

Offset: 2

Author

Antti Karttunen, Mar 18 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..6381 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A156552, A329697, A322993, A342652, A350067.

Cf. A000040 (positions of 0's), A350069 (of 1's).

Programs

PARI

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};
A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
A342651(n) = A329697(A156552(n));

PARI

\\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt
v156552sigs = readvec("a156552.txt");
A329697(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A329697(f[k,1]-1)))); };
A342651(n) = if(isprime(n),0,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); sum(i=2-(ps[1]%2),#ps,es[i]*(1+A329697(ps[i]-1)))); \\ Antti Karttunen, Jan 29 2022

Formula

a(n) = A329697(A156552(n)) = A329697(A322993(n)).

a(n) = A329697(A342666(n)) + A342656(n).

a(p) = 0 for all primes p.

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