A337800 Numbers of the form (2^i)*(3^j) or (2^i)*(5^j).

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 25, 27, 32, 36, 40, 48, 50, 54, 64, 72, 80, 81, 96, 100, 108, 125, 128, 144, 160, 162, 192, 200, 216, 243, 250, 256, 288, 320, 324, 384, 400, 432, 486, 500, 512, 576, 625, 640, 648, 729, 768, 800, 864, 972, 1000

Offset: 1

Author

Vaclav Kotesovec, Sep 22 2020

Keywords

• nonn
• easy

Comments

Union of A003586 and A003592.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Graph - the asymptotic ratio (64000000 terms)

Crossrefs

Cf. A003586, A003592, A257997, A258023, A337801.

Programs

Mathematica

n = 10^4; Join[Table[2^i*3^j, {i, 0, Log[2, n]}, {j, 0, Log[3, n/2^i]}], Table[2^i*5^j, {i, 0, Log[2, n]}, {j, 0, Log[5, n/2^i]}]] // Flatten // Union (* Amiram Eldar, Sep 23 2020 *)

Formula

a(n) ~ exp(sqrt(2*log(2)*log(3)*log(5)*n / log(15))) / sqrt(2).

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