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A081061
Union of 3-smooth numbers and prime powers.
4
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 04 2003
STATUS
approved