A137794 Characteristic function of numbers having no prime gaps in their factorization.

1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1

Offset: 1

Author

Reinhard Zumkeller, Feb 11 2008

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for characteristic functions

Crossrefs

Cf. A137721 (partial sums).

Programs

Mathematica

a[n_] := With[{pp = PrimePi @ FactorInteger[n][[All, 1]]},
     Boole[pp[[-1]] - pp[[1]] + 1 == Length[pp]]];
Array[a, 105] (* Jean-François Alcover, Dec 09 2021 *)

PARI

A137794(n) = if(1>=omega(n),1,my(pis=apply(primepi,factor(n)[,1])); for(k=2,#pis,if(pis[k]>(1+pis[k-1]),return(0))); (1)); \\ Antti Karttunen, Sep 27 2018

Formula

a(n) = 0^A073490(n).

a(A073491(n)) = 1; a(A073492(n)) = 0;

a(n) = A137721(n) - A137721(n-1) for n>1.