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%I #15 Mar 19 2020 06:13:52
%S 1,9,21,25,33,35,49,65,69,77,81,115,121,129,133,143,145,161,169,203,
%T 209,217,253,259,261,265,273,275,289,295,297,299,301,305,319,321,323,
%U 329,341,361,377,385,391,403,415,427,437,451,481,505,513,515,517,527,529
%N A positive integer k is included if no prime divisor p of k, when p is represented in binary, occurs within k represented in binary.
%C This sequence contains no primes.
%C This sequence contains no even numbers (A014076). - _Robert G. Wilson v_, Sep 22 2008
%H Amiram Eldar, <a href="/A143791/b143791.txt">Table of n, a(n) for n = 1..10000</a>
%e 21 is binary is 10101. The prime divisors of 21 are 3 and 7. 3 is 11 in binary, which does not occur within 10101. 7 is 111 in binary, which also does not occur within 10101. So 21 is in the sequence.
%e On the other hand, 27 in binary is 11011. The only prime divisor of 27 is 3, which is 11 in binary. 11 does occur (twice) within 11011 like so: (11)0(11). So 27 is not in the sequence.
%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@ 1000, f@# == 0 &] (* _Robert G. Wilson v_, Sep 22 2008 *)
%Y Cf. A143792.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Sep 01 2008
%E a(7) and further terms from _Robert G. Wilson v_, Sep 22 2008
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