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A081061 Union of 3-smooth numbers and prime powers.

%I A081061 #14 Sep 16 2024 12:47:54
%S A081061 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 A081061 43,47,48,49,53,54,59,61,64,67,71,72,73,79,81,83,89,96,97,101,103,107,
%U A081061 108,109,113,121,125,127,128,131,137,139,144,149,151,157,162,163,167
%N A081061 Union of 3-smooth numbers and prime powers.
%C A081061 A081060(m)=1 iff m=a(k) for some k.
%C A081061 Complement of A081062.
%H A081061 Jean-François Alcover, <a href="/A081061/b081061.txt">Table of n, a(n) for n = 1..10000</a>
%t A081061 smooth3Q[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1;
%t A081061 Select[Range[1000], PrimePowerQ[#] || smooth3Q[#]&] (* _Jean-François Alcover_, Oct 14 2021 *)
%o A081061 (Python)
%o A081061 from sympy import integer_log, primepi, integer_nthroot
%o A081061 def A081061(n):
%o A081061     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 A081061     m, k = n, f(n)
%o A081061     while m != k: m, k = k, f(k)
%o A081061     return m # _Chai Wah Wu_, Sep 16 2024
%Y A081061 Cf. A003586, A000961, A081060, A081062, A081063.
%K A081061 nonn
%O A081061 1,2
%A A081061 _Reinhard Zumkeller_, Mar 04 2003