A081061 - OEIS

%I #14 Sep 16 2024 12:47:54

%S 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,

%T 43,47,48,49,53,54,59,61,64,67,71,72,73,79,81,83,89,96,97,101,103,107,

%U 108,109,113,121,125,127,128,131,137,139,144,149,151,157,162,163,167

%N Union of 3-smooth numbers and prime powers.

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

%C Complement of A081062.

%H Jean-François Alcover, <a href="/A081061/b081061.txt">Table of n, a(n) for n = 1..10000</a>

%t smooth3Q[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1;

%t Select[Range[1000], PrimePowerQ[#] || smooth3Q[#]&] (* _Jean-François Alcover_, Oct 14 2021 *)

%o (Python)

%o from sympy import integer_log, primepi, integer_nthroot

%o def A081061(n):

%o     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)))

%o     m, k = n, f(n)

%o     while m != k: m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Sep 16 2024

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

%K nonn,changed

%O 1,2

%A _Reinhard Zumkeller_, Mar 04 2003