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.

15, 27, 39, 45, 51, 55, 57, 63, 75, 85, 87, 91, 93, 95, 99, 105, 111, 117, 119, 123, 125, 135, 141, 147, 153, 155, 159, 165, 171, 175, 177, 183, 185, 187, 189, 195, 201, 205, 207, 213, 215, 219, 221, 225, 231, 235, 237, 243, 245, 247, 249, 255, 267, 279, 285

Offset: 1

Author

Robert G. Wilson v, Oct 03 2008

Keywords

• easy
• nonn
• base

Comments

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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A014076, A143791.

Programs

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