A277569 Numbers k such that k/6^m == 3 (mod 6), where 6^m is the greatest power of 6 that divides k.

3, 9, 15, 18, 21, 27, 33, 39, 45, 51, 54, 57, 63, 69, 75, 81, 87, 90, 93, 99, 105, 108, 111, 117, 123, 126, 129, 135, 141, 147, 153, 159, 162, 165, 171, 177, 183, 189, 195, 198, 201, 207, 213, 219, 225, 231, 234, 237, 243, 249, 255, 261, 267, 270, 273, 279

Offset: 1

Author

Clark Kimberling, Nov 01 2016

Keywords

• nonn
• easy

Comments

Positions of 3 in A277544.

Numbers having 3 as rightmost nonzero digit in base 6. This is one sequence in a 5-way splitting of the positive integers; the other four are indicated in the Mathematica program. Every term is a multiple of 3; see A277573.

Numbers m having the property that tau(3m) < tau(2m) where tau(m) = A000005(m) (i.e., the number of divisors of m). - Gary Detlefs, Jan 28 2019

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A277544, A277567, A277568, A277573.

Programs

Maple

with(numtheory): for n from 1 to 279 do if tau(3*n)Gary Detlefs, Jan 28 2019

Mathematica

z = 260; a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, z}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[6, 1] (* A277567 *)
p[6, 2] (* A277568 *)
p[6, 3] (* this sequence *)
p[6, 4] (* A277570 *)
p[6, 5] (* A277571 *)

PARI

is(n)=(n/6^valuation(n,6))%6==3 \\ Charles R Greathouse IV, Nov 03 2016

Formula

a(n) = 5n + O(log n). - Charles R Greathouse IV, Nov 03 2016