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A073484
Number of gaps in factors of the n-th squarefree number.
8
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
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
Sequence in context: A121361 A191907 A052343 * A203947 A081396 A194293
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 03 2002
STATUS
approved