A145195 - OEIS

A145195

Odd composite numbers n with property that at least one prime divisor p of n is a substring of the binary representation of n.

%I #13 Sep 17 2017 22:33:01

%S 15,27,39,45,51,55,57,63,75,85,87,91,93,95,99,105,111,117,119,123,125,

%T 135,141,147,153,155,159,165,171,175,177,183,185,187,189,195,201,205,

%U 207,213,215,219,221,225,231,235,237,243,245,247,249,255,267,279,285

%N Odd composite numbers n with property that at least one prime divisor p of n is a substring of the binary representation of n.

%C It is obvious that all even numbers and all prime numbers would meet this criterion.

%H G. C. Greubel, <a href="/A145195/b145195.txt">Table of n, a(n) for n = 1..5000</a>

%e 15 is 1111_2 and 15=3*5 where 3 is 11_2, so 15 is a term.

%t 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; Select[ Range@ 286, !PrimeQ@ # && OddQ@ # && f@# > 0 &]

%Y Cf. A014076, A143791.

%K easy,nonn,base

%O 1,1

%A _Robert G. Wilson v_, Oct 03 2008