A102550 Number of distinct prime-factors of n that are bitwise covered by n.

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

Offset: 1

Author

Reinhard Zumkeller, Jan 14 2005

Keywords

• nonn

Comments

p is bitwise covered by n iff (p = (n AND p)) bitwise: A080099(n,p)=p.

Links

• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A001221 (omega), A007088, A004676, A080099, A102210.

Cf. A102551, A102553, A102554, A102555.

Programs

Mathematica

a[1] = 0; a[k_] := Module[{f=FactorInteger[k][[;; , 1]]}, Count[BitAnd[k, f]-f, 0]];  Array[a,120] (* Amiram Eldar, Feb 06 2019 *)

Formula

a(A102553(n)) = A001221(A102553(n));

a(A102554(n)) < A001221(A102554(n));

a(A102551(n)) = 0, a(A102551(n)) > 0;

a(A102555(n)) = n;

a(m) < n for m < A102555(n).

a(n) = Sum_{p|n} (binomial(n,p) mod 2), where p is a prime. - Ridouane Oudra, May 03 2019

Extensions

Offset 1 from Amiram Eldar, Feb 06 2019