A236575 Number of primes between successive numbers that are not squarefree.

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

Offset

1,1

Comments

It seems that a(n) <= 2. [This is true since the maximal gap between nonsquarefree numbers is 4 and 1 in every 3 consecutive numbers is divisible by 3. - Amiram Eldar, Feb 09 2021]

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

A013929(n) = 4, 8, 9, 12, 16, 18, 20, ...
a(1) = 2 because there exists 2 primes between 4 and 8;
a(2) = 0 because there are no prime between 8 and 9;
a(3) = 1 because there exists 1 prime between 9 and 12.

Maple

sqf:={}:t:= n-> product(ithprime(k), k=1..n): for n from 1 to 400 do:if t(n) mod n <>0 then sqf:=sqf union {n} fi od:n1:=nops(sqf):
for m from 1 to n1-1 do :c:=0:i1 :=sqf[m] :i2 :=sqf[m+1] :for p from i1+1 to i2-1 do:if type(p, prime)=true then c:=c+1:else fi:od: printf(`%d, `, c):od:

Mathematica

lst={}; aa={}; bb={}; Do[If[MemberQ[aa, EulerPhi[n]/n], AppendTo[bb, n], AppendTo[aa, EulerPhi[n]/n]], {n, 1, 1000}]; Do[p=0; Do[If[PrimeQ[a], p++], {a, bb[[n]]+1, bb[[n+1]]-1}]; AppendTo[lst, p], {n, 100}]; lst

Crossrefs

Cf. A013929.

Sequence in context: A123230 A078821 A125184 * A059282 A114591 A161849

Adjacent sequences: A236572 A236573 A236574 * A236576 A236577 A236578

Keyword

nonn

Author

Michel Lagneau, Jan 29 2014

Status

approved