A374484 Index of A006899(n) in A003586.

1, 2, 3, 4, 6, 7, 9, 12, 13, 17, 19, 22, 27, 28, 34, 37, 41, 48, 49, 56, 62, 65, 74, 77, 84, 93, 95, 106, 111, 118, 130, 131, 143, 152, 157, 171, 175, 186, 199, 202, 218, 225, 235, 252, 253, 271, 281, 290, 309, 312, 329, 344, 350, 371, 378, 393, 413, 416, 439

Offset: 1

Author

Chai Wah Wu, Sep 16 2024

Keywords

• nonn
• easy

Comments

Index of powers of 2 and 3 in 3-smooth numbers.

Examples

			A006899(10) = 64 which is the 17th term of A003586, therefore a(10) = 17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A006899.

Disjoint union of A022330 and A022331.

Programs

Mathematica

seq[lim_] := Position[Times @@ IntegerExponent[#, {2, 3}] & /@ Sort[Flatten[ Table[2^i*3^j, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}] ]], 0] // Flatten; seq[10^11] (* Amiram Eldar, Sep 18 2024 *)

Python

from sympy import integer_log
def A374484(n): return sum(((1<
				

Formula

A003586(a(n)) = A006899(n).

a(n) ~ c * n^2, where c = log(2)*log(3)/(2*(log(2) + log(3))^2) = 0.118598856384648... - Vaclav Kotesovec and Amiram Eldar, Sep 19 2024