OFFSET
1,2
COMMENTS
Old name: a(n) = (1/3)*(s(n+1) - 1), where s = A026224.
Conjectures based on old name: these are numbers of the form (3*i+1)*3^j; see A182828, and they comprise the complement of A026179, except for the initial 1 in A026179.
From Peter Munn, Mar 17 2022: (Start)
Numbers with an even number of prime factors of the form 3k-1 counting repetitions.
Numbers whose squarefree part is congruent to 1 modulo 3 or 3 modulo 9.
The integers in an index 2 subgroup of the positive rationals under multiplication. As such the sequence is closed under multiplication and - where the result is an integer - under division; also for any positive integer k not in the sequence, the sequence's complement is generated by dividing by k the terms that are multiples of k.
Alternatively, the sequence can be viewed as an index 2 subgroup of the positive integers under the commutative binary operation A059897(.,.).
Viewed either way, the sequence corresponds to a subgroup of the quotient group derived in the corresponding way from A055047.
(End)
The asymptotic density of this sequence is 1/2. - Amiram Eldar, Apr 03 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Squarefree Part.
FORMULA
MATHEMATICA
a[b_] := Table[Mod[n/b^IntegerExponent[n, b], b], {n, 1, 160}]
p[b_, d_] := Flatten[Position[a[b], d]]
p[3, 1] (* A026225 *)
p[3, 2] (* A026179 without initial 1 *)
(* Clark Kimberling, Oct 19 2016 *)
PROG
(PARI) isok(m) = core(m) % 3 == 1 || core(m) % 9 == 3; \\ Peter Munn, Mar 17 2022
CROSSREFS
Elements of array A182828 in ascending order.
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
New name from Peter Munn, Mar 17 2022
STATUS
approved