A215659 Values of k such that k*(k - 1) is a primorial number.

2, 3, 6, 15, 715

Offset: 1

Author

Jonathan Sondow, Sep 07 2012

Keywords

• nonn
• more

Comments

Values of k in A215658.

See A161620 for the primorial values. - Jeppe Stig Nielsen, Mar 27 2018

Links

• Carol Nelson, David E. Penney and Carl Pomerance, 714 and 715, J. Recreational Math. 7:2 (1994), pp. 87-89.

Crossrefs

Cf. A215658, A161620.

Programs

Mathematica

Select[Range[10^5], Product[Prime@ i, {i, PrimeNu@ #}] == # &[# (# - 1)] &] (* Michael De Vlieger, Apr 10 2018 *)

Python

from sympy import primorial, integer_nthroot
A215659_list = []
for i in range(1,10**2):
    a, b = integer_nthroot(4*primorial(i)+1,2)
    if b:
        A215659_list.append((a+1)//2) # Chai Wah Wu, Apr 01 2021

Formula

a(n) * (a(n) - 1) = A215658(n)#, where p# = 2 * 3 * 5 * 7 * 11 * ... * p is a primorial, the product of the primes from 2 to p.

Extensions

Name improved by Jeppe Stig Nielsen, Mar 27 2018