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A342652
a(n) = A331410(A156552(n)).
2
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
2,5
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.
FORMULA
a(n) = A331410(A156552(n)).
a(p) = 0 for all primes p.
a(A003961(n)) = a(n).
PROG
(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)))); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 18 2021
STATUS
approved