%I A002827 M4268 N1783
%S A002827 6,60,90,87360,146361946186458562560000
%N A002827 Unitary perfect numbers: usigma(n)-n = n.
%C A002827 d is a unitary divisor of n if gcd(d,n/d)=1; usigma(n) is their sum (A034448).
%C A002827 The prime factors of a unitary perfect number (A002827) are the Higgs 
               primes (A057447). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Oct 
               10 2005
%D A002827 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002827 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002827 R. K. Guy, Unsolved Problems in Number Theory, Sect. B3.
%D A002827 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section III.45.1.
%D A002827 M. V. Subbarao, T. J. Cook, R. S. Newberry and J. M. Weber, On unitary 
               perfect numbers, Delta, 3 (No. 1, 1972), 22-26.
%D A002827 C. R. Wall, The fifth unitary perfect number, Canad. Math. Bull., 18 
               (1975), 115-122.
%D A002827 C. R. Wall, On the largest odd component of a unitary perfect number, 
               Fib. Quart., 25 (1987), 312-316.
%H A002827 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               UnitaryPerfectNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A002827 G. Villemin's Almanac of Numbers, <a href="http://membres.lycos.fr/villemingerard/
               Decompos/ParfUnit.htm">Nombres Unitairement Parfaits</a>
%H A002827 Wikipedia, <a href="http://en.wikipedia.org/wiki/Unitary_perfect_number">
               Unitary perfect number</a>
%e A002827 Unitary divisors of 60 are 1,4,3,5,12,20,15,60, with sum 120 = 2*60.
%e A002827 146361946186458562560000 = 2^18 * 3 * 5^4 * 7 * 11 * 13 * 19 * 37 * 79 
               * 109 * 157 * 313
%Y A002827 Cf. A034460, A034448.
%Y A002827 Cf. A002827, A057447.
%Y A002827 Sequence in context: A074452 A007358 A007357 this_sequence A137498 A036283 
               A126576
%Y A002827 Adjacent sequences: A002824 A002825 A002826 this_sequence A002828 A002829 
               A002830
%K A002827 nonn,nice,hard
%O A002827 1,1
%A A002827 N. J. A. Sloane (njas(AT)research.att.com).