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

1,1

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

Formula

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

Maple

with(numtheory): for n from 1 to 279 do if tau(3*n)<tau(2*n) then print(n) fi od # 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 *)

Prog

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

Crossrefs

Cf. A277544, A277567, A277568, A277573.

Sequence in context: A100331 A155764 A259754 * A310329 A310330 A071123

Adjacent sequences: A277566 A277567 A277568 * A277570 A277571 A277572

Keyword

nonn,easy

Author

Clark Kimberling, Nov 01 2016

Status

approved