cp's OEIS Frontend

A195238 Numbers with at least 2 and not more than 3 distinct prime factors not greater than 7 that are multiples of 7 or of 15.

%I A195238 #17 Oct 25 2024 06:50:59
%S A195238 14,15,21,28,30,35,42,45,56,60,63,70,75,84,90,98,105,112,120,126,135,
%T A195238 140,147,150,168,175,180,189,196,224,225,240,245,252,270,280,294,300,
%U A195238 315,336,350,360,375,378,392,405,441,448,450,480,490,504,525,540,560
%N A195238 Numbers with at least 2 and not more than 3 distinct prime factors not greater than 7 that are multiples of 7 or of 15.
%C A195238 A143204 is a subsequence.
%C A195238 Subsequence of A002473.
%H A195238 Reinhard Zumkeller, <a href="/A195238/b195238.txt">Table of n, a(n) for n = 1..1000</a>
%F A195238 2 <= A001221(a(n)) <= 3.
%F A195238 5 <= A006530(a(n)) <= 7.
%F A195238 Sum_{n>=1} 1/a(n) = 11/16. - _Amiram Eldar_, Oct 25 2024
%e A195238 a(10) = 60 = 2^2 * 3 * 5.
%e A195238 a(11) = 63 = 3^2 * 7.
%e A195238 a(12) = 70 = 2 * 5 * 7.
%t A195238 pfsQ[n_]:=Module[{fs=Transpose[FactorInteger[n]][[1]]},Max[fs]<8 && 1<Length[fs]<4]; upto=3000;With[{max7=Floor[upto/7],max15= Floor[ upto/15]},Union[Select[Join[7Range[max7],15Range[max15]],pfsQ]]] (* _Harvey P. Dale_, Aug 21 2011 *)
%o A195238 (Haskell)
%o A195238 a195238 n = a195238_list !! (n-1)
%o A195238 a195238_list = filter (\x -> a001221 x `elem` [2,3] &&
%o A195238                              a006530 x `elem` [5,7] &&
%o A195238                              (mod x 7 == 0 || mod x 15 == 0)) [1..]
%o A195238 -- _Reinhard Zumkeller_, Sep 13 2011
%o A195238 (PARI) is(n)=my(v=apply(p->valuation(n,p), [2,3,5,7])); n==2^v[1]*3^v[2]*5^v[3]*7^v[4] && (v[4] || v[2]*v[3]) && factorback(v)==0 && !!v[1]+!!v[2]+!!v[3]+!!v[4]>1 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A195238 Cf. A001221, A006530, A143204, A002473.
%K A195238 nonn,easy
%O A195238 1,1
%A A195238 _Harvey P. Dale_, Sep 13 2011