login
A100713
Hyperperfect brilliant numbers.
1
21, 697, 1333, 1909, 3901, 96361, 130153, 163201, 2708413, 2768581, 4013833, 4312681, 4658449, 6392257, 7478041, 8766061, 8883841, 9427657, 9699181, 12064333, 14489437, 15042553, 16260901, 16904101, 18116737, 21396313, 28005301, 29751229, 31837801, 36640993
OFFSET
1,1
REFERENCES
Richard K. Guy, "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.
Joe Roberts, The Lure of the Integers, Washington, DC: Math. Assoc. Amer., p. 177, 1992.
LINKS
Judson S. McCranie, A Study of Hyperperfect Numbers. J. Integer Sequences 3, No. 00.1.3, 2000.
Daniel Minoli, Issues in Nonlinear Hyperperfect Numbers, Math. Comput., Vol. 34, No. 150 (1980), pp. 639-645.
Eric Weisstein's World of Mathematics, Hyperperfect Number.
FORMULA
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jonathan Vos Post, Dec 11 2004
EXTENSIONS
More terms from Amiram Eldar, Dec 01 2020
STATUS
approved