A061400 Primes p such that there is no squarefree number between p and the next prime.
2, 3, 11, 17, 59, 71, 97, 107, 149, 179, 191, 197, 227, 239, 269, 311, 347, 349, 419, 431, 521, 599, 659, 809, 827, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1277, 1319, 1427, 1447, 1451, 1487, 1607, 1619, 1663, 1667, 1787, 1871, 1931, 1949, 1997, 2027, 2087
Offset: 1
Keywords
Examples
Between 71 and 73, the only composite is 72 = 2*2*2*3*3, not squarefree. Each of the integers between 97 and 101 has at least one squared divisor.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
Programs
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Maple
with(numtheory): a:=proc(n) local p,B,j: p:=ithprime(n): B:={}: for j from 1 to p-1 do if abs(mobius(j))>0 then B:=B union {j} else B:=B fi od: B[nops(B)] end: A:=[seq(a(m),m=1..400)]: b:=proc(k) if isprime(A[k])=true then A[k] else fi end: seq(b(i),i=1..400); # Emeric Deutsch, Oct 14 2005 -
Mathematica
Select[Prime@ Range@ 310, Count[Range[# + 1, NextPrime@ # - 1], k_ /; SquareFreeQ@ k] == 0 &] (* Michael De Vlieger, Feb 19 2017 *)
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PARI
{ n=0; p=2; forprime (q=3, 109621, c=0; for (i=p+1, q-1, c+=issquarefree(i); if (c, break)); if (c==0, write("b061400.txt", n++, " ", p)); p=q ) } \\ Harry J. Smith, Jul 22 2009
Extensions
Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar
Comments