A324816 Binary weight of A324815; number of 1-bits in common positions in 2*A156552(n) and A323243(n).

0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 0, 3, 2, 1, 1, 1, 0, 1, 0, 0, 2, 3, 1, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 1, 0, 0, 0, 2, 3, 0, 1, 1, 1, 0, 1, 0, 1, 1

Offset: 1

Author

Antti Karttunen, Mar 17 2019

Keywords

• nonn

Comments

Numbers 0 .. 7 occur for the first time in 1, 4, 9, 54, 162, 972, 2816, 3456. These are also the positions of records so far.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000120, A156552, A323243, A324201, A324815.

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 by David A. Corneth
A324816(n) = hammingweight(bitand(2*A156552(n),A323243(n))); \\ Needs code also from A323243.

Formula

a(n) = A000120(A324815(n)).

a(p) = 0 for all primes p.

a(A324201(n)) = A000043(n).