Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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