OFFSET
1,6
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
Between 113 and 127 the 6 squarefree numbers are 114, 115, 118, 119, 122, 123, so a(30)=6.
MAPLE
p:= 2:
for n from 1 to 200 do
q:= nextprime(p);
A[n]:= nops(select(numtheory:-issqrfree, [$p+1..q-1]));
p:= q;
od:
seq(A[i], i=1..200); # Robert Israel, Jan 06 2017
MATHEMATICA
a[n_] := Count[Range[Prime[n]+1, Prime[n+1]-1], _?SquareFreeQ];
Array[a, 100] (* Jean-François Alcover, Feb 28 2019 *)
Count[Range[#[[1]]+1, #[[2]]-1], _?(SquareFreeQ[#]&)]&/@Partition[ Prime[ Range[120]], 2, 1] (* Harvey P. Dale, Oct 14 2021 *)
PROG
(PARI) { n=0; q=2; forprime (p=3, prime(1001), a=0; for (i=q+1, p-1, a+=issquarefree(i)); write("b061398.txt", n++, " ", a); q=p ) } \\ Harry J. Smith, Jul 22 2009
(PARI) a(n) = my(pp=prime(n)+1); sum(k=pp, nextprime(pp)-1, issquarefree(k)); \\ Michel Marcus, Feb 28 2019
(Python)
from math import isqrt
from sympy import mobius, prime, nextprime
def A061398(n):
p = prime(n)
q = nextprime(p)
r = isqrt(p-1)+1
return sum(mobius(k)*((q-1)//k**2) for k in range(r, isqrt(q-1)+1))+sum(mobius(k)*((q-1)//k**2-(p-1)//k**2) for k in range(1, r))-1 # Chai Wah Wu, Jun 01 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 07 2001
STATUS
approved