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A100713 Hyperperfect brilliant numbers.

%I A100713 #19 Feb 16 2025 08:32:55
%S A100713 21,697,1333,1909,3901,96361,130153,163201,2708413,2768581,4013833,
%T A100713 4312681,4658449,6392257,7478041,8766061,8883841,9427657,9699181,
%U A100713 12064333,14489437,15042553,16260901,16904101,18116737,21396313,28005301,29751229,31837801,36640993
%N A100713 Hyperperfect brilliant numbers.
%D A100713 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.
%D A100713 Joe Roberts, The Lure of the Integers, Washington, DC: Math. Assoc. Amer., p. 177, 1992.
%H A100713 Amiram Eldar, <a href="/A100713/b100713.txt">Table of n, a(n) for n = 1..2678</a>
%H A100713 Judson S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A Study of Hyperperfect Numbers.</a> J. Integer Sequences 3, No. 00.1.3, 2000.
%H A100713 Daniel Minoli, <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0559206-9">Issues in Nonlinear Hyperperfect Numbers</a>, Math. Comput., Vol. 34, No. 150 (1980), pp. 639-645.
%H A100713 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperperfectNumber.html">Hyperperfect Number</a>.
%F A100713 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.
%e A100713 21 = 3 * 7, 697 = 17 * 41, 1333 = 31 * 43, 1909 = 23 * 83, 3901 = 47 * 83, 96361 = 173 * 557, 130153 = 157 * 829, 163201 = 293 * 557.
%e A100713 a(2) = 697 because 697 is a 12-hyperperfect number, A028500(2) and is a brilliant number because 697 = 17 * 41.
%Y A100713 Cf. A007592, A078972, A001358.
%K A100713 nonn,base
%O A100713 1,1
%A A100713 _Jonathan Vos Post_, Dec 11 2004
%E A100713 More terms from _Amiram Eldar_, Dec 01 2020