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

1,15

Comments

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

Links

Table of n, a(n) for n=1..105.

Index entries for sequences related to binary expansion of n

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

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 *)

Crossrefs

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

Cf. A102551, A102553, A102554, A102555.

Sequence in context: A095408 A357375 A133008 * A293139 A351319 A213725

Adjacent sequences: A102547 A102548 A102549 * A102551 A102552 A102553

Keyword

nonn

Author

Reinhard Zumkeller, Jan 14 2005

Extensions

Offset 1 from Amiram Eldar, Feb 06 2019

Status

approved