A143204 Union of A143207 and A033847.

14, 28, 30, 56, 60, 90, 98, 112, 120, 150, 180, 196, 224, 240, 270, 300, 360, 392, 448, 450, 480, 540, 600, 686, 720, 750, 784, 810, 896, 900, 960, 1080, 1200, 1350, 1372, 1440, 1500, 1568, 1620, 1792, 1800, 1920, 2160, 2250, 2400, 2430, 2700, 2744, 2880

Offset: 1

Author

Reinhard Zumkeller, Aug 12 2008

Keywords

• nonn
• easy

Comments

Subsequence of A195238. - Harvey P. Dale, Sep 13 2011

Examples

			a(1)  =  14 = 2 * 7 = A033847(1).
a(2)  =  28 = 2^2 * 7 = A033847(2).
a(3)  =  30 = 2 * 3 * 5 = A143207(1).
a(4)  =  56 = 2^3 * 7 = A033847(3).
a(5)  =  60 = 2^2 * 3 * 5 = A143207(2).
a(6)  =  90 = 2 * 3^2 * 5 = A143207(3).
a(7)  =  98 = 2 * 7^2 = A033847(4).
a(8)  = 112 = 2^4 * 7 = A033847(5).
a(9)  = 120 = 2^3 * 3 * 5 = A143207(4).
a(10) = 150 = 2 * 3 * 5^2 = A143207(5).
a(11) = 180 = 2^2 * 3^2 * 5 = A143207(6).
a(12) = 196 = 2^2 * 7^2 = A033847(6).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033847, A143201, A143207, A195238.

Programs

Mathematica

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 *)

Formula

A143201(a(n)) = 6. - Harvey P. Dale, Sep 13 2011

Sum_{n>=1} 1/a(n) = 7/24. - Amiram Eldar, Oct 25 2024

Extensions

Corrected by Harvey P. Dale, Aug 21 2011

Revised version with improved definition; thanks to Harvey P. Dale, who noticed that the original definition was not sufficient.