A081061 Union of 3-smooth numbers and prime powers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 23, 24, 25, 27, 29, 31, 32, 36, 37, 41, 43, 47, 48, 49, 53, 54, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 96, 97, 101, 103, 107, 108, 109, 113, 121, 125, 127, 128, 131, 137, 139, 144, 149, 151, 157, 162, 163, 167

Offset

1,2

Comments

A081060(m)=1 iff m=a(k) for some k.

Complement of A081062.

Links

Jean-François Alcover, Table of n, a(n) for n = 1..10000

Mathematica

smooth3Q[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1;
Select[Range[1000], PrimePowerQ[#] || smooth3Q[#]&] (* Jean-François Alcover, Oct 14 2021 *)

Prog

(Python)
from sympy import integer_log, primepi, integer_nthroot
def A081061(n):
    def f(x): return int(n+x-1+(a:=x.bit_length())+(b:=integer_log(x, 3)[0])-sum((x//3**i).bit_length() for i in range(b+1))-sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, a)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 16 2024

Crossrefs

Cf. A003586, A000961, A081060, A081062, A081063.

Sequence in context: A242413 A243068 A342339 * A317589 A141807 A246422

Adjacent sequences: A081058 A081059 A081060 * A081062 A081063 A081064

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2003

Status

approved