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

1,1

Comments

All the terms are divisible by 3 by definition.

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

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

A055777 is a subsequence.

Cf. A007949, A336069.

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

Sequence in context: A067759 A331068 A310122 * A319451 A256882 A191267

Adjacent sequences: A336065 A336066 A336067 * A336069 A336070 A336071

Keyword

nonn

Author

Amiram Eldar, Jul 07 2020

Status

approved