A108513 Numbers of the form (2^i)*(5^j)*(7^k), with i, j, k >= 0.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49, 50, 56, 64, 70, 80, 98, 100, 112, 125, 128, 140, 160, 175, 196, 200, 224, 245, 250, 256, 280, 320, 343, 350, 392, 400, 448, 490, 500, 512, 560, 625, 640, 686, 700, 784, 800, 875, 896, 980, 1000, 1024, 1120

Offset: 1

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jul 05 2005

Keywords

• nonn
• easy

Comments

Numbers m | 70^e with integer e >= 0. - Michael De Vlieger, Aug 22 2019

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051037, A108319, A108347, A003592, A003591, A003595.

Programs

Mathematica

With[{n = 1120}, Sort@ Flatten@ Table[2^i * 5^j * 7^k, {i, 0, Log2@ n}, {j, 0, Log[5, n/2^i]}, {k, 0, Log[7, n/(2^i*5^j)]}]] (* Michael De Vlieger, Aug 22 2019 *)

PARI

isok(n) = (n/(2^valuation(n,2)*5^valuation(n,5)*7^valuation(n,7)) == 1); \\ Michel Marcus, Oct 01 2013

Formula

Sum_{n>=1} 1/a(n) = (2*5*7)/((2-1)*(5-1)*(7-1)) = 35/12. - Amiram Eldar, Sep 23 2020

a(n) ~ exp((6*log(2)*log(5)*log(7)*n)^(1/3)) / sqrt(70). - Vaclav Kotesovec, Sep 23 2020