A061743 Numbers k such that k! is divisible by (k+1)^2.

11, 14, 15, 17, 19, 20, 23, 24, 26, 27, 29, 31, 32, 34, 35, 38, 39, 41, 43, 44, 47, 48, 49, 50, 51, 53, 54, 55, 56, 59, 62, 63, 64, 65, 67, 68, 69, 71, 74, 75, 76, 77, 79, 80, 83, 84, 86, 87, 89, 90, 91, 92, 94, 95, 97, 98, 99, 101, 103, 104, 107, 109, 110, 111, 113, 114

Offset: 1

Author

Robert G. Wilson v, Jun 21 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A001751, A060462, A178156, A264848.

Programs

Mathematica

Select[Range[120], IntegerQ[ #!/(# + 1)^2] &]

PARI

{ n=0; f=1; for (a=1, 2588, f*=a; if (f%(a + 1)^2 == 0, write("b061743.txt", n++, " ", a)) ) } \\ Harry J. Smith, Jul 27 2009

PARI

isok(k) = !(k! % (k+1)^2); \\ Michel Marcus, Jul 01 2018

Python

from sympy import primepi
def A061743(n):
    def f(x): return int(n+2+primepi(x+1)+primepi(x+1>>1))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Oct 17 2024

Formula

a(n) = A264828(n+3)-1. Complement of {A178156} - 1. - Chai Wah Wu, Oct 17 2024