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

Author

Antti Karttunen, Apr 14 2019

Keywords

• nonn

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.

Examples

			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.
		

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

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.

Programs

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));

Formula

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