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A002827 Unitary perfect numbers: usigma(n)-n = n.
(Formerly M4268 N1783)
10
6, 60, 90, 87360, 146361946186458562560000 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

d is a unitary divisor of n if gcd(d,n/d)=1; usigma(n) is their sum (A034448).

The prime factors of a unitary perfect number (A002827) are the Higgs primes (A057447). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Oct 10 2005

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, Sect. B3.

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section III.45.1.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. V. Subbarao, T. J. Cook, R. S. Newberry and J. M. Weber, On unitary perfect numbers, Delta, 3 (No. 1, 1972), 22-26.

C. R. Wall, The fifth unitary perfect number, Canad. Math. Bull., 18 (1975), 115-122.

C. R. Wall, On the largest odd component of a unitary perfect number, Fib. Quart., 25 (1987), 312-316.

LINKS

G. Villemin's Almanac of Numbers, Nombres Unitairement Parfaits

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Wikipedia, Unitary perfect number

EXAMPLE

Unitary divisors of 60 are 1,4,3,5,12,20,15,60, with sum 120 = 2*60.

146361946186458562560000 = 2^18 * 3 * 5^4 * 7 * 11 * 13 * 19 * 37 * 79 * 109 * 157 * 313

CROSSREFS

Cf. A034460, A034448.

Cf. A002827, A057447.

Sequence in context: A189000 A007358 A007357 * A137498 A036283 A126576

Adjacent sequences:  A002824 A002825 A002826 * A002828 A002829 A002830

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 14 04:29 EST 2012. Contains 205570 sequences.