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

Author

Jonathan Vos Post, Dec 11 2004

Keywords

• nonn
• base

Examples

			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.
		

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.

Crossrefs

Cf. A007592, A078972, A001358.

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.

Extensions

More terms from Amiram Eldar, Dec 01 2020