A161769 - OEIS

%I #10 May 27 2019 04:12:03

%S 4,15,16,21,27,28,33,35,39,42,48,51,52,55,57,60,64,65,69,72,76,77,78,

%T 84,85,87,90,91,93,95,98,105,108,110,111,114,115,119,120,123,124,126,

%U 129,132,133,135,140,141,143,145,148,150,155,156,159,161,162,170,172,175

%N A positive integer n is included if the greatest common divisor of (the sum of the distinct primes dividing n) and (the sum of the exponents in the prime-factorization of n) is > 1.

%C n is included if A161606(n) is >= 2.

%e The prime factorization of 28 is 2^2 * 7^1. The sum of the distinct prime divisors of 28 is 2+7 = 9. The sum of the prime-factorization exponents of 28 is 2+1 = 3. Since gcd(9,3) = 3 is > 1, then 28 is included in this sequence.

%t okQ[n_]:=Module[{fitr=Transpose[FactorInteger[n]]},GCD[Plus@@First[fitr],Plus@@Last[fitr]]>1];Select[Range[500], okQ] (* _Harvey P. Dale_, Jan 24 2010 *)

%Y Cf. A008472, A001222, A161606.

%K nonn

%O 1,1

%A _Leroy Quet_, Jun 18 2009

%E More terms from _Harvey P. Dale_, Jan 24 2010