A024556 Odd squarefree composite numbers.

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

Zak Seidov, Table of n, a(n) for n = 1..11999.

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.

Cf. A010051, A046388, A078837.

Sequence in context: A329229 A390639 A146166 * A046388 A056913 A002557

Adjacent sequences: A024553 A024554 A024555 * A024557 A024558 A024559

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2000

Extensions

More terms from James Sellers, May 22 2000

Status

approved