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

1,9

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)

Formula

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

a(p) = 0 for all primes p.

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

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

Crossrefs

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

Sequence in context: A324868 A363622 A287066 * A321448 A334158 A116357

Adjacent sequences: A324813 A324814 A324815 * A324817 A324818 A324819

Keyword

nonn

Author

Antti Karttunen, Mar 17 2019

Status

approved