A309396 Number of lucky numbers <= n!.

1, 1, 1, 2, 7, 26, 115, 614, 3866, 28339, 237017, 2227657, 23233568, 266201749

Offset: 0

Author

Hauke Löffler, Jul 28 2019

Keywords

• nonn
• hard
• more

Examples

			a(1) = 1 because there is one lucky number (1) <= 1 (1!).
a(3) = 2 because there are two lucky numbers (1, 3) <= 6 (3!).
		

Crossrefs

Cf. A000959, A003604, A309399, A000142.

Programs

SageMath

def lucky(n):
  L=list(range(1, n+1, 2)); j=1
  while L[j] <= len(L)-1:
    L=[L[i] for i in range(len(L)) if (i+1)%L[j]!=0]
    j+=1
  return(L)
A000959=lucky(factorial(10))
def lucky_range(a,b):
    lucky = []
    for l in A000959:
        if l >= b:
            return lucky
        if l>=a: lucky.append(l)
[ len(lucky_range(0,factorial(n)+1)) for n in range(10) ]

Extensions

a(10)-a(12) from Giovanni Resta, May 10 2020

a(13) from Kevin P. Thompson, Nov 24 2021