cp's OEIS Frontend

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

%I A236575 #11 Feb 09 2021 02:36:45
%S A236575 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,
%T A236575 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,
%U A236575 0,1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,1
%N A236575 Number of primes between successive numbers that are not squarefree.
%C A236575 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]
%H A236575 Michel Lagneau, <a href="/A236575/b236575.txt">Table of n, a(n) for n = 1..10000</a>
%e A236575 A013929(n) = 4, 8, 9, 12, 16, 18, 20, ...
%e A236575 a(1) = 2 because there exists 2 primes between 4 and 8;
%e A236575 a(2) = 0 because there are no prime between 8 and 9;
%e A236575 a(3) = 1 because there exists 1 prime between 9 and 12.
%p A236575 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):
%p A236575 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:
%t A236575 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
%Y A236575 Cf. A013929.
%K A236575 nonn
%O A236575 1,1
%A A236575 _Michel Lagneau_, Jan 29 2014