A368249 a(n) = A002378(A005117(n)-1).

0, 2, 6, 20, 30, 42, 90, 110, 156, 182, 210, 272, 342, 420, 462, 506, 650, 812, 870, 930, 1056, 1122, 1190, 1332, 1406, 1482, 1640, 1722, 1806, 2070, 2162, 2550, 2756, 2970, 3192, 3306, 3422, 3660, 3782, 4160, 4290, 4422, 4692, 4830, 4970, 5256, 5402, 5852, 6006

Offset: 1

Author

Amiram Eldar, Dec 19 2023

Keywords

• nonn
• easy

Comments

The squarefree oblong numbers (A229882) are all terms of this sequence, and their relative asymptotic density in it is A065474/A059956 = 0.530711... (A065469).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002378, A005117, A229882.

Cf. A059956, A065469, A065474, A368250.

Programs

Mathematica

Table[n*(n - 1), {n, Select[Range[100], SquareFreeQ]}]

PARI

lista(kmax) = forsquarefree(k=1, kmax, print1(k[1]*(k[1]-1), ", "));

Python

from math import isqrt
from sympy import mobius
def A368249(n):
    def f(x): return int(n-sum(mobius(k)*(x//k**2) for k in range(2, isqrt(x)+1)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m*(m-1) # Chai Wah Wu, Dec 23 2024

Formula

Sum_{n>=2} 1/a(n) = Sum_{k>=2} (zeta(k)/zeta(2*k) - 1) = 0.848633... (A368250).