1,1

Guy, R. K. "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." Section B2 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-53, 1994.

Minoli, D. "Issues in Nonlinear Hyperperfect Numbers." Math. Comput. 34, 639-645, 1980.

Roberts, J. The Lure of the Integers. Washington, DC: Math. Assoc. Amer., p. 177, 1992.

McCranie, J. S., A Study of Hyperperfect Numbers. J. Integer Sequences 3, No. 00.1.3, 2000.

Eric Weisstein's World of Mathematics, Hyperperfect Number.

a(n) is an element in the intersection of A007592 and A078972. a(n)=m(sigma(a(n))-a(n)-1)+1 for some m>1 and a(n) is a semiprime with the same number of digits in each prime factor.

21 = 3 * 7, 697 = 17 * 41, 1333 = 31 * 43, 1909 = 23 * 83, 3901 = 47 * 83, 96361 = 173 * 557, 130153 = 157 * 829, 163201 = 293 * 557.

a(2) = 697 because 697 is a 12-hyperperfect number, A028500(2) and is a brilliant number because 697 = 17 * 41.

Cf. A007592, A078972, A001358.

Sequence in context: A158216 A020246 A006934 this_sequence A056565 A009167 A012479

Adjacent sequences: A100710 A100711 A100712 this_sequence A100714 A100715 A100716

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 11 2004