A336068 Numbers k such that the exponent of the highest power of 3 dividing k (A007949) is a divisor of k.

3, 6, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 48, 51, 54, 57, 60, 66, 69, 72, 75, 78, 84, 87, 90, 93, 96, 102, 105, 108, 111, 114, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 156, 159, 165, 168, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204

Offset: 1

Author

Amiram Eldar, Jul 07 2020

Keywords

• nonn

Comments

All the terms are divisible by 3 by definition.

Šalát (1994) proved that the asymptotic density of this sequence is 0.287106... (A336069).

Examples

			3 is a term since A007949(3) = 1 is a divisor of 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Tibor Šalát, On the function a_p, p^a_p(n) || n (n > 1), Mathematica Slovaca, Vol. 44, No. 2 (1994), pp. 143-151.

Crossrefs

A055777 is a subsequence.

Cf. A007949, A336069.

Similar sequences: A033950, A005349, A006446, A074946, A075592, A007694, A112249, A336066.

Programs

Mathematica

Select[Range[200], Mod[#, 3] == 0 && Divisible[#, IntegerExponent[#, 3]] &]

PARI

isok(m) = if (!(m%3), (m % valuation(m,3)) == 0); \\ Michel Marcus, Jul 08 2020