A143204 - OEIS

%I #27 Oct 25 2024 06:23:35

%S 14,28,30,56,60,90,98,112,120,150,180,196,224,240,270,300,360,392,448,

%T 450,480,540,600,686,720,750,784,810,896,900,960,1080,1200,1350,1372,

%U 1440,1500,1568,1620,1792,1800,1920,2160,2250,2400,2430,2700,2744,2880

%N Union of A143207 and A033847.

%C Subsequence of A195238. - _Harvey P. Dale_, Sep 13 2011

%H Reinhard Zumkeller, <a href="/A143204/b143204.txt">Table of n, a(n) for n = 1..10000</a>

%F A143201(a(n)) = 6. - _Harvey P. Dale_, Sep 13 2011

%F Sum_{n>=1} 1/a(n) = 7/24. - _Amiram Eldar_, Oct 25 2024

%e a(1)  =  14 = 2 * 7 = A033847(1).

%e a(2)  =  28 = 2^2 * 7 = A033847(2).

%e a(3)  =  30 = 2 * 3 * 5 = A143207(1).

%e a(4)  =  56 = 2^3 * 7 = A033847(3).

%e a(5)  =  60 = 2^2 * 3 * 5 = A143207(2).

%e a(6)  =  90 = 2 * 3^2 * 5 = A143207(3).

%e a(7)  =  98 = 2 * 7^2 = A033847(4).

%e a(8)  = 112 = 2^4 * 7 = A033847(5).

%e a(9)  = 120 = 2^3 * 3 * 5 = A143207(4).

%e a(10) = 150 = 2 * 3 * 5^2 = A143207(5).

%e a(11) = 180 = 2^2 * 3^2 * 5 = A143207(6).

%e a(12) = 196 = 2^2 * 7^2 = A033847(6).

%t q[n_] := Module[{p1 = {2, 3, 5}, p2 = {2, 7}, e1, e2}, e1 = IntegerExponent[n, p1]; e2 = IntegerExponent[n, p2]; (Times @@ e1 > 0 && Times @@ (p1^e1) == n) || (Times @@ e2 > 0 && Times @@ (p2^e2) == n)]; Select[Range[3000], q] (* _Amiram Eldar_, Oct 25 2024 *)

%Y Cf. A033847, A143201, A143207, A195238.

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Aug 12 2008

%E Corrected by _Harvey P. Dale_, Aug 21 2011

%E Revised version with improved definition; thanks to _Harvey P. Dale_, who noticed that the original definition was not sufficient.