1,1

Related to hyperperfect numbers of a certain form.

Contribution from Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009: (Start)

Minoli defined the sequences and concepts that follow in the 1980 IEEE paper below:

- For t=2 to infinity, the sequence m(n,t) = n exp(t) - (n-1) is called a Mersenne Sequence Rooted on n

- If n is prime, this sequence is called a Legitimate Mersenne Sequence

- Any j belonging to the sequence m(n,t) is called a Generalized Mersenne Number (n-GMN)

- If j belonging to the sequence m(n,t) is prime, it is then called a n-Generalized Mersenne Prime (n-GMP).

Note: m(n,t) = n*m(n,t-1) + n exp(2) - 2*n+1.

These numbers play a role in the context of hyperperfect numbers.

(End)

Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009]

Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (p.114-134) [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009]

Daniel Minoli, Robert Bear, Hyperperfect Numbers, PME (Pi Mu Epsilon) Journal, University Oklahoma, Fall 1975, pp. 153-157. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 27 2009]

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3

Sequence in context: A166707 A116525 A094623 this_sequence A015446 A083177 A110466

Adjacent sequences: A034919 A034920 A034921 this_sequence A034923 A034924 A034925

nonn

Jud McCranie (j.mccranie(AT)comcast.net)