A379968 Characteristic function of A279029, numbers k with the property that the smallest and the largest Dyck path of the symmetric representation of sigma(k) do not share line segments.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

a(n) = [A279228(n) = 0], where [ ] is the Iverson bracket.

Mathematica

(* Function a279029Q[] is defined in A279029 *)
a379968[n_] := Map[Boole[a279029Q[#]]&, Range[n]]
a379968[128] (* Hartmut F. W. Hoft, Feb 20 2025 *)

Prog

(PARI)
A365429(n) = { my(d=divisors(n)); for(i=2, #d, if(d[i]>2*d[i-1], return(0))); (1); };
A379968(n) = if(A365429(n), 1, my(f=factor(n), p=f[#f~, 1], q=n/p); (f[#f~, 2]<=1 && (p == 1+2*q) && A365429(q)));

Crossrefs

Characteristic function of A279029.

Sum of A365429 (which is characteristic function of A174973) and characteristic function of A262259.

Cf. A237593, A279029, A279228, A365429, A379968.

Sequence in context: A380536 A370122 A117198 * A271047 A054525 A174852

Adjacent sequences: A379965 A379966 A379967 * A379969 A379970 A379971

Keyword

nonn

Author

Antti Karttunen, Jan 12 2025

Status

approved