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A061400 Primes p such that there is no squarefree number between p and the next prime. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes in sequence A112925. - Leroy Quet, Oct 06 2005

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

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.

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 *)

PROG

(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

CROSSREFS

Cf. A005117, A013929.

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

Sequence in context: A051078 A051090 A263933 * A090474 A263934 A263935

Adjacent sequences:  A061397 A061398 A061399 * A061401 A061402 A061403

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 07 2001

EXTENSIONS

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)