A189716 Numbers k such that A156595(k-1) = 1; complement of A189715.

2, 3, 5, 8, 11, 12, 14, 17, 18, 20, 21, 23, 26, 27, 29, 30, 32, 35, 38, 39, 41, 44, 45, 47, 48, 50, 53, 56, 57, 59, 62, 65, 66, 68, 71, 72, 74, 75, 77, 80, 83, 84, 86, 89, 92, 93, 95, 98, 99, 101, 102, 104, 107, 108, 110, 111, 113, 116, 119, 120, 122, 125, 126, 128, 129, 131, 134, 137, 138, 140, 143, 146, 147, 149, 152, 153, 155, 156, 158

Offset

1,1

Comments

See A156595.

Numbers whose squarefree part is congruent modulo 9 to 2, 3, 5 or 8. - Peter Munn, May 17 2020

The asymptotic density of this sequence is 1/2. - Amiram Eldar, Mar 08 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

(See A189715.)
f[p_, e_] := (p^Mod[e, 2]); sqfpart[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[160], MemberQ[{2, 3, 5, 8}, Mod[sqfpart[#], 9]] &] (* Amiram Eldar, Mar 08 2021 *)

Prog

(Python)
from sympy import integer_log
def A189716(n):
    def f(x): return n+x-sum(((m:=x//9**i)-2)//9+(m-5)//9+(m-8)//9+(m-3)//9+4 for i in range(integer_log(x, 9)[0]+1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 15 2025

Crossrefs

Cf. A007913, A156595, A189715, A189717.

Union of A055041 and A055048.

Sequence in context: A276731 A028891 A028890 * A002480 A173672 A303024

Adjacent sequences: A189713 A189714 A189715 * A189717 A189718 A189719

Keyword

nonn

Author

Clark Kimberling, Apr 26 2011

Extensions

Name enhanced by Peter Munn, May 17 2020

Status

approved