%I #11 Jan 29 2022 20:14:45

%S 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,

%T 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,

%U 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

%N a(n) = A329697(A156552(n)).

%H Antti Karttunen, <a href="/A342651/b342651.txt">Table of n, a(n) for n = 2..6381</a> (based on Hans Havermann's factorization of A156552)

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

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

%F a(p) = 0 for all primes p.

%F a(A003961(n)) = a(n).

%o (PARI)

%o 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};

%o 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)))); };

%o A342651(n) = A329697(A156552(n));

%o (PARI)

%o \\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt

%o v156552sigs = readvec("a156552.txt");

%o 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)))); };

%o 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

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

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

%K nonn

%O 2,7

%A _Antti Karttunen_, Mar 18 2021