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A061400 Primes p such that there is no squarefree number between p and the next prime. 7

%I #26 Sep 07 2017 02:43:14

%S 2,3,11,17,59,71,97,107,149,179,191,197,227,239,269,311,347,349,419,

%T 431,521,599,659,809,827,881,1019,1031,1049,1061,1091,1151,1277,1319,

%U 1427,1447,1451,1487,1607,1619,1663,1667,1787,1871,1931,1949,1997,2027,2087

%N Primes p such that there is no squarefree number between p and the next prime.

%C Primes in sequence A112925. - _Leroy Quet_, Oct 06 2005

%H Harry J. Smith, <a href="/A061400/b061400.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%p 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

%t Select[Prime@ Range@ 310, Count[Range[# + 1, NextPrime@ # - 1], k_ /; SquareFreeQ@ k] == 0 &] (* _Michael De Vlieger_, Feb 19 2017 *)

%o (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

%Y Cf. A005117, A013929.

%Y Cf. A112925, A112926, A112928, A112929, A112930.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 07 2001

%E Edited by _N. J. A. Sloane_, Aug 23 2008 at the suggestion of _R. J. Mathar_

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)