

A143792


a(n) = the number of distinct prime divisors, p, of n that, when p is represented in binary, each p occurs at least once in the binary representation of n.


3



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

1,6


COMMENTS

a(2^k * p) = 2, where k = any positive integer and p = any odd prime.
a(p) = 1, where p = any prime.
a(2^k) = 1, where k = any positive integer.
a(n) <= A078826(n).  Reinhard Zumkeller, Sep 08 2008
Size of intersection of nth rows of tables A225243 and A027748.  Reinhard Zumkeller, Aug 14 2013


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


EXAMPLE

60 in binary is 111100. The distinct primes dividing 60 are 2 (which is 10 in binary), 3 (11 in binary) and 5 (101) in binary. The string 10 does occur within 111100 like so: 111(10)0. The string 11 also occurs (multiple times) within 111100, in one way like so: (11)1100. But the string 101 does not occur in 111100. Since 2 and 3 occur within 60 (when each of these numbers is written in binary), but 5 does not, then a(60) = 2.


MATHEMATICA

f[n_] := Block[{nb = ToString@ FromDigits@ IntegerDigits[n, 2], psb = ToString@ FromDigits@ IntegerDigits[ #, 2] & /@ First@ Transpose@ FactorInteger@ n, c = 0, k = 1}, lmt = 1 + Length@ psb; While[k < lmt, If[ StringCount[nb, psb[[k]]] > 0, c++ ]; k++ ]; c]; f[1] = 0; Array[f, 105] (* Robert G. Wilson v, Sep 22 2008 *)


PROG

(Haskell)
import Data.List (intersect)
a143792 n = length $ a225243_row n `intersect` a027748_row (fromIntegral n)
 Reinhard Zumkeller, Aug 14 2013


CROSSREFS

Cf. A143791.
Sequence in context: A277487 A144032 A137686 * A230121 A029375 A071462
Adjacent sequences: A143789 A143790 A143791 * A143793 A143794 A143795


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Sep 01 2008


EXTENSIONS

More terms from Robert G. Wilson v, Sep 22 2008


STATUS

approved



