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%I #24 Sep 01 2020 17:09:31
%S 1,2,3,4,5,6,6,7,8,9,9,10,10,10,11,12,12,13,13,14,14,14,14,15,16,16,
%T 17,17,17,18,18,19,19,19,19,20,20,20,20,21,21,21,21,21,22,22,22,23,23,
%U 24,24,24,24,25,25,25,25,25,25,26,26,26,26,27,27,27,27,27,27,27,27,28,28
%N Number of 5-smooth numbers (A051037) <= n.
%C A 5-smooth number is a number of the form 2^x*3^y*5^z (x,y,z) >= 0.
%F a(n) = Card{ k | A051037(k) <= n }.
%F Asymptotically : let a = 1/(6*log(2)*log(3)*log(5)) and b = sqrt(30) then a(n) = a*log(b*n)^3 + O(log(n)).
%F a(n) = -Sum_{k=1,n} mu(30*k)*floor(n/k). - _Benoit Cloitre_, Jun 14 2007
%F a(n) = Sum_{i=0..floor(log_5(n))} Sum_{j=0..floor(log_3(n/5^i))} floor(log_2(2*n/(5^i*3^j))). - _Ridouane Oudra_, Jul 17 2020
%o (PARI) for(n=1,100,print1(sum(k=1,n,if(sum(i=4,n,if(k%prime(i),0,1)),0,1)),","))
%o (PARI) a(n)=-sum(k=1,n,moebius(2*3*5*k)*floor(n/k)) \\ _Benoit Cloitre_, Jun 14 2007
%Y Cf. A051037, A106598, A112751.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Jun 02 2002
%E Title corrected by _Rainer Rosenthal_, Aug 30 2020
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