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URL: https://oeis.org/A024556

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A024556
Odd squarefree composite numbers.
30
15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 105, 111, 115, 119, 123, 129, 133, 141, 143, 145, 155, 159, 161, 165, 177, 183, 185, 187, 195, 201, 203, 205, 209, 213, 215, 217, 219, 221, 231, 235, 237, 247, 249, 253, 255, 259, 265, 267, 273
OFFSET
1,1
COMMENTS
Composite numbers n such that Sum_{k=1..n-1} floor(k^3/n) = (1/4)*(n-2)*(n^2-1) (equality also holds for all primes). - Benoit Cloitre, Dec 08 2002
LINKS
Eric Weisstein's World of Mathematics, Lehmer's Constant
Eric Weisstein's World of Mathematics, Prime Sums
FORMULA
a(n) = (Pi^2/4)*n + O(n/log n). - Charles R Greathouse IV, Mar 12 2025
MATHEMATICA
Complement[Select[Range[3, 281, 2], SquareFreeQ], Prime[Range[PrimePi[281]]]] (* Harvey P. Dale, Jan 26 2011 *)
PROG
(Haskell)
a024556 n = a024556_list !! (n-1)
a024556_list = filter ((== 0) . a010051) $ tail a056911_list
-- Reinhard Zumkeller, Apr 12 2012
(PARI) is(n)=n>1&&n%2&&!isprime(n)&&issquarefree(n) \\ Charles R Greathouse IV, Apr 12 2012
(PARI) forstep(n=3, 273, 2, k=omega(n); if(k>1&&bigomega(n)==k, print1(n, ", "))) \\ Hugo Pfoertner, Dec 19 2018
(Python)
from math import isqrt
from sympy import primepi, mobius
def A024556(n):
def f(x): return int(n+x+primepi(x)-sum(mobius(k)*(x//k**2+1>>1) for k in range(1, isqrt(x)+1, 2)))
m, k = n+1, f(n+1)
while m != k: m, k = k, f(k)
return m # Chai Wah Wu, Nov 25 2025
CROSSREFS
Intersection of A056911 and A071904.
Subsequence of A061346.
Sequence in context: A329229 A390639 A146166 * A046388 A056913 A002557
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 22 2000
EXTENSIONS
More terms from James Sellers, May 22 2000
STATUS
approved