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%I #23 Dec 27 2022 02:26:38
%S 1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,
%T 1,1,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,0,
%U 0,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0
%N a(n) = if n is 7-smooth then 1 else 0: characteristic function of 7-smooth numbers.
%H Reinhard Zumkeller, <a href="/A086299/b086299.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.
%F Multiplicative with: a(p) = if p<=7 then 1 else 0, p prime.
%F a(A002473(n)) = 1; a(A068191(n)) = 0. - _Reinhard Zumkeller_, Apr 01 2012
%F Dirichlet g.f.: 1/((1-2^(-s))*(1-3^(-s))*(1-5^(-s))*(1-7^(-s))). - _Amiram Eldar_, Dec 27 2022
%t Table[If[Max[Transpose[FactorInteger[n]][[1]]]<11,1,0],{n,110}] (* _Harvey P. Dale_, Oct 08 2013 *)
%t smooth7Q[n_] := n == Times@@({2, 3, 5, 7}^IntegerExponent[n, {2, 3, 5, 7}]);
%t a[n_] := Boole[smooth7Q[n]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Oct 17 2021 *)
%o (Haskell)
%o a086299 = fromEnum . (<= 7) . a006530 -- _Reinhard Zumkeller_, Apr 01 2012
%Y Cf. A002473, A006530, A068191.
%K nonn,mult
%O 1,1
%A _Reinhard Zumkeller_, Jul 15 2003
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