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A236575
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Number of primes between successive numbers that are not squarefree.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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