Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A002827
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A002827 Unitary perfect numbers: usigma(n)-n = n.
(Formerly M4268 N1783)
+0
10
6, 60, 90, 87360, 146361946186458562560000 (list; graph; listen)
OFFSET

1,1

COMMENT

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.

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

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

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

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: A074452 A007358 A007357 this_sequence A137498 A036283 A126576

Adjacent sequences: A002824 A002825 A002826 this_sequence A002828 A002829 A002830

KEYWORD

nonn,nice,hard

AUTHOR

njas

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified July 23 17:35 EDT 2008. Contains 142285 sequences.


AT&T Labs Research