A016048 Least k such that (2*p_n)*k + 1 | Mersenne(p_n), p_n = n-th prime, n >= 2.

1, 3, 9, 1, 315, 3855, 13797, 1, 4, 34636833, 3, 163, 5, 25, 60, 1525, 18900352534538475, 1445580, 1609, 3, 17, 1, 3477359660913989536233495, 59, 36793758459, 12379533, 758220919762679268184943973309, 3421967, 15

Offset: 2

Author

Robert G. Wilson v

Keywords

• nonn

Comments

M(p_n) = 2^p_n - 1 = (2*p_n)*j + 1 = [(2*p_n)*k_1 + 1] ... [(2*p_n)*k_i + 1], n >= 2 (i.e., odd prime p_n), i >= 1. Then k = Min(k_1, ..., k_i).

Links

• Chris K. Caldwell, Modular restrictions on Mersenne divisors

Crossrefs

Cf. A000040, A016047.

Formula

a(n) = (A016047(n) - 1) / (2*A000040(n)). - Jeppe Stig Nielsen, Jul 18 2014

Extensions

Definition edited, comment added by Daniel Forgues, Oct 06 2009