A073484 Number of gaps in factors of the n-th squarefree number.

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 2, 0

Offset

1,69

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(A000040(n))=0; a(A006094(n))=0; a(A002110(n))=0; a(A073485(n))=0.

a(A073486(n))>0; a(A073487(n))=1; a(A073488(n))=2; a(A073489(n))=3.

a(n)=0 iff A073483(n)=1.

Example

The 69th squarefree number is 110=2*5*11, therefore a(69)=2, as there are two gaps: between 2 and 5 and between 5 and 11.

Mathematica

gaps[n_] := SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 != NextPrime[p1], Overlaps -> True]; gaps /@ Select[Range[200], SquareFreeQ] (* Amiram Eldar, Apr 10 2021 *)

Crossrefs

Cf. A005117, A073483.

Sequence in context: A121361 A191907 A052343 * A203947 A081396 A194293

Adjacent sequences: A073481 A073482 A073483 * A073485 A073486 A073487

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2002

Status

approved