A324912 Binary weight of A324911(n).

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 2, 1, 1, 1, 3, 1

Offset

1,4

Comments

After 1 differs from A051903 at n = 900, 1764, 1800, 2700, 3528, 4356, 4500, 4900, 5292, ..., which seems to be a subsequence of A318720.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A000120(A324911(n)).

Example

For n = 900 = 2^2 * 3^2 * 5^2, A324911(900) = A156552(4) * A156552(9) * A156552(25) = 3*6*12 = 216, which in base-2 is written as "11011000", thus a(900) = 4.

Prog

(PARI)
A156552(n) = { my(f = factor(n), 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 }; \\ From A156552
A324911(n) = { my(f=factor(n)); prod(i=1, #f~, A156552(f[i, 1]^f[i, 2])); };
A324912(n) = hammingweight(A324911(n));

Crossrefs

Cf. A000120, A051903, A156552, A318720, A324911.

Differs from A072411 for the first time at n=72, where a(72) = 3, while A072411(72) = 6.

Sequence in context: A070013 A070014 A051903 * A157754 A072411 A290107

Adjacent sequences: A324909 A324910 A324911 * A324913 A324914 A324915

Keyword

nonn

Author

Antti Karttunen, Apr 14 2019

Status

approved