A128693 Numbers of the form 3^k*p, where 1 <= k <= 6 and p is a prime different from 3.

6, 15, 18, 21, 33, 39, 45, 51, 54, 57, 63, 69, 87, 93, 99, 111, 117, 123, 129, 135, 141, 153, 159, 162, 171, 177, 183, 189, 201, 207, 213, 219, 237, 249, 261, 267, 279, 291, 297, 303, 309, 321, 327, 333, 339, 351, 369, 381, 387, 393, 405, 411, 417, 423, 447

Offset: 1

Author

Klaus Brockhaus, Mar 26 2007

Keywords

• nonn

Comments

Auxiliary sequence for A128694 which gives the number of groups of order a(n).

a(n) is a subset of the composite numbers m having the property that tau(3*m)=tau(m)+2, where tau(m)=A000005(m) (the number of divisors of m). All primes except 3 satisfy this property. - Gary Detlefs, Jan 25 2019

Examples

			135 = 3^3*5 is a term.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A128694.

Programs

Magma

[ n: n in [1..450] | #t eq 2 and ((t[1, 1] eq 2 and t[1, 2] eq 1 and t[2, 1] eq 3 and t[2, 2] le 6) or (t[1, 1] eq 3 and t[1, 2] le 6 and t[2, 2] eq 1)) where t is Factorization(n) ];