A086299 a(n) = if n is 7-smooth then 1 else 0: characteristic function of 7-smooth numbers.

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

• nonn
• mult

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Smooth Number.
• Index entries for characteristic functions.

Crossrefs

Cf. A002473, A006530, A068191.

Programs

Haskell

a086299 = fromEnum . (<= 7) . a006530  -- Reinhard Zumkeller, Apr 01 2012

Mathematica

Table[If[Max[Transpose[FactorInteger[n]][[1]]]<11,1,0],{n,110}] (* Harvey P. Dale, Oct 08 2013 *)
smooth7Q[n_] := n == Times@@({2, 3, 5, 7}^IntegerExponent[n, {2, 3, 5, 7}]);
a[n_] := Boole[smooth7Q[n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 17 2021 *)

Formula

Multiplicative with: a(p) = if p<=7 then 1 else 0, p prime.

a(A002473(n)) = 1; a(A068191(n)) = 0. - Reinhard Zumkeller, Apr 01 2012

Dirichlet g.f.: 1/((1-2^(-s))*(1-3^(-s))*(1-5^(-s))*(1-7^(-s))). - Amiram Eldar, Dec 27 2022