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

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

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

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

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

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 *)

Prog

(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

Crossrefs

Cf. A137721 (partial sums).

Sequence in context: A368992 A334465 A054527 * A357731 A336546 A209929

Adjacent sequences: A137791 A137792 A137793 * A137795 A137796 A137797

Keyword

nonn

Author

Reinhard Zumkeller, Feb 11 2008

Status

approved