A130632 Number of natural numbers between d(n) and d(n+1), where d(n) denotes the number of divisors of n.

0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 3, 3, 1, 0, 0, 2, 3, 3, 3, 1, 0, 1, 5, 4, 0, 0, 1, 3, 5, 5, 3, 1, 0, 0, 4, 6, 1, 0, 3, 5, 5, 5, 3, 0, 1, 1, 7, 6, 2, 1, 1, 3, 5, 3, 3, 3, 0, 1, 9, 9, 1, 1, 0, 2, 3, 5, 3, 1, 3, 5, 9, 9, 1, 1, 0, 1, 3, 5, 7, 4, 0, 1, 9, 7, 0, 0, 3, 5, 9, 7, 1, 1, 0, 0, 7, 9, 3, 0, 2, 6, 5, 5, 5, 0, 3

Offset

1,11

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = max(0, |A051950(n+1)| - 1). - R. J. Mathar, Jun 28 2010

Maple

A051950 := proc(n) if n = 0 then 1; else numtheory[tau](n+1)-numtheory[tau](n) ; end if; end proc:
A130632 := proc(n) local g ; g := abs(A051950(n)) ; max(0, g-1) ; end proc:
seq(A130632(n), n=1..80) ;
# R. J. Mathar, Jun 28 2010

Mathematica

Array[Max[0, Abs[DivisorSigma[0, #]-DivisorSigma[0, #+1]]-1]&, 105] (* James C. McMahon, Feb 11 2025 *)

Prog

(PARI) a(n) = max(0, abs(numdiv(n+1)-numdiv(n))-1); \\ Michel Marcus, Aug 24 2015

Crossrefs

Cf. A000005, A051950.

Sequence in context: A205826 A131193 A350479 * A229158 A290454 A281066

Adjacent sequences: A130629 A130630 A130631 * A130633 A130634 A130635

Keyword

nonn

Author

Giovanni Teofilatto, Aug 11 2007

Extensions

More terms from R. J. Mathar, Jun 28 2010

Extended up to a(105) by Antti Karttunen, Oct 07 2017

Status

approved