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

1,1

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.

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

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 *)

Prog

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

Crossrefs

Cf. A002473, A006530, A068191.

Sequence in context: A136522 A352871 A188641 * A131364 A152066 A334946

Adjacent sequences: A086296 A086297 A086298 * A086300 A086301 A086302

Keyword

nonn,mult

Author

Reinhard Zumkeller, Jul 15 2003

Status

approved