A100713 Hyperperfect brilliant numbers.

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

Amiram Eldar, Table of n, a(n) for n = 1..2678

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

Cf. A007592, A078972, A001358.

Sequence in context: A339119 A243746 A276021 * A056565 A187359 A009167

Adjacent sequences: A100710 A100711 A100712 * A100714 A100715 A100716

Keyword

nonn,base

Author

Jonathan Vos Post, Dec 11 2004

Extensions

More terms from Amiram Eldar, Dec 01 2020

Status

approved