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A077381
Number of squarefree numbers between successive squares (exclusive).
1
2, 3, 5, 5, 7, 8, 8, 11, 11, 14, 14, 14, 17, 19, 18, 20, 22, 20, 24, 26, 28, 26, 28, 30, 31, 32, 33, 36, 34, 37, 40, 36, 43, 42, 44, 46, 47, 46, 49, 48, 48, 51, 50, 56, 55, 57, 58, 60, 63, 59, 63, 63, 63, 69, 70, 67, 71, 71, 73, 71, 74, 78, 76, 78, 81, 79, 84, 83, 87, 85, 84, 87
OFFSET
1,1
LINKS
Gabriel Mincu and Laurenţiu Panaitopol, On some properties of squarefree and squareful numbers, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 49 (97), No. 1 (2006), pp. 63-68; alternative link.
FORMULA
From Amiram Eldar, Feb 16 2021: (Start)
a(n) > n for all n (Mincu and Panaitopol, 2006).
a(n) ~ (12/Pi^2) * n. (End)
EXAMPLE
a(1) = 2 because there are 2 squarefree integers between 1^2 and 2^2: 2 and 3.
a(3) = 5 = number of squarefree numbers between 3^2 and 4^2: 10, 11, 13, 14 and 15.
MAPLE
a:= n-> nops(select(numtheory[issqrfree], [$n^2+1..(n+1)^2-1])):
seq(a(n), n=1..80); # Alois P. Heinz, Jul 16 2019
MATHEMATICA
Table[Count[Range[n^2 + 1, (n + 1)^2 - 1], _?(SquareFreeQ[#] &)], {n, 1, 80}]
(* Harvey P. Dale, Jan 25 2014 *)
PROG
(PARI) a(n)=s=0; for(i=n^2+1, (n+1)^2, if(issquarefree(i), s=s+1)); return(s); \\ corrected by Hugo Pfoertner, Jul 16 2019
CROSSREFS
Sequence in context: A168065 A077724 A163867 * A225636 A023838 A246795
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 06 2002
EXTENSIONS
More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 23 2004
Name clarified by Hugo Pfoertner, Jul 16 2019
STATUS
approved