A342652 a(n) = A331410(A156552(n)).

0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 3, 2, 3, 0, 2, 0, 3, 2, 3, 0, 2, 1, 4, 1, 3, 0, 2, 0, 1, 3, 4, 2, 3, 0, 5, 3, 3, 0, 4, 0, 4, 2, 6, 0, 2, 1, 4, 4, 4, 0, 4, 2, 3, 4, 7, 0, 3, 0, 7, 3, 3, 3, 3, 0, 5, 5, 3, 0, 4, 0, 8, 2, 5, 2, 4, 0, 3, 3, 8, 0, 5, 3, 11, 6, 5, 0, 4, 2, 5, 7, 8, 4, 5, 0, 2, 3, 4, 0, 6, 0, 4, 2

Offset: 2

Author

Antti Karttunen, Mar 18 2021

Keywords

• nonn

Comments

Positions of ones is given by a subsequence of A053810, i.e., prime powers whose exponent is one of the primes in A000043. See also A324201, A335431.

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000043, A003961, A053810, A156552, A324201, A331410, A335431, A342651.

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};
A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
A342652(n) = A331410(A156552(n));

Formula

a(n) = A331410(A156552(n)).

a(p) = 0 for all primes p.

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