Search: id:A018892
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%I A018892
%S A018892 1,2,2,3,2,5,2,4,3,5,2,8,2,5,5,5,2,8,2,8,5,5,2,11,3,5,4,8,2,14,2,6,5,5,
               5,
%T A018892 13,2,5,5,11,2,14,2,8,8,5,2,14,3,8,5,8,2,11,5,11,5,5,2,23,2,5,8,7,5,14,
               2,
%U A018892 8,5,14,2,18,2,5,8,8,5,14,2,14,5,5,2,23,5,5,5,11,2,23,5,8,5,5,5,17,2,8,
               8
%N A018892 Number of ways to write 1/n as a sum of exactly 2 unit fractions.
%C A018892 a(n) =(tau(n^2)+1)/2. Number of elements in the set {(x,y): x|n, y|n, 
               x<=y, GCD(x,y)=1}. Number of divisors of n^2 less than or equal to 
               n. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 03 2002
%C A018892 Equivalently number of pairs (x,y) such that LCM(x,y)=n - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), May 16 2002
%C A018892 Number of right triangles with an integer hypotenuse and height n. - 
               Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 10 2002
%C A018892 Number of solutions to x^3==n^2 (mod x) 1<=x<=n - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Aug 19 2002
%C A018892 Except for the initial term, each entry is at least equal to 2 because 
               of the identities 1/n=1/2n + 1/2n=1/(n+1) + 1/n*(n+1). - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), May 04 2004
%D A018892 K. S. Brown, Posting to netnews group sci.math, Aug 17 1996.
%D A018892 L. E. Dickson, History of The Theory of Numbers, Vol. 2 p. 690, Chelsea 
               NY 1923.
%D A018892 Problem 1051(a), American Mathematical Monthly, Vol. 105, No. 4, 1998 
               p. 372.
%D A018892 A. M. & I. M. Yaglom, Challenging Mathematical Problems With Elementary 
               Solutions, Vol. 1 pp. 8;60 Prob. 19 Dover NY
%H A018892 T. D. Noe, <a href="b018892.txt">Table of n, a(n) for n=1..10000</a>
%H A018892 Jorg Brown, <a href="a018894.txt">Comparison of records in sigma(n)/phi(n) 
               and A018892</a>
%F A018892 If n = (p1^a1)(p2^a2)...(pt^at), a(n) = ((2 a1 + 1)(2 a2 + 1) ... (2 
               at + 1) + 1)/2.
%F A018892 a(n)=A063647(n)+1=A046079(2n)+1. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Dec 01 2003
%e A018892 Examples:
%e A018892 n=1: 1/1 = 1/2 + 1/2.
%e A018892 n=2: 1/2 = 1/4 + 1/4 = 1/3 + 1/6.
%e A018892 n=3: 1/3 = 1/6 + 1/6 = 1/4 + 1/12.
%t A018892 f[j_, n_] := (Times @@ (j(Last /@ FactorInteger[n]) + 1) + j - 1)/j; 
               Table[f[2, n], {n, 96}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Aug 03 2005)
%o A018892 (PARI) A018892(n)=(numdiv(n^2)+1)/2 - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Dec 30 2007
%o A018892 (PARI) A018892s(n)=local(t=divisors(n^2));vector((#t+1)/2,i,[n+t[i],n+n^2/
               t[i]]) /* show solutions */ - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Dec 30 2007
%Y A018892 Records: A126097, A126098. Cf. A048691, A063647.
%Y A018892 Sequence in context: A160273 A141822 A033099 this_sequence A100565 A010846 
               A073023
%Y A018892 Adjacent sequences: A018889 A018890 A018891 this_sequence A018893 A018894 
               A018895
%K A018892 nonn,easy,nice
%O A018892 1,2
%A A018892 Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A018892 More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 15, 
               1996
%E A018892 First example corrected by Jason Orendorff (jason.orendorff(AT)gmail.com), 
               Jan 02 2009
%E A018892 Incorrect Mathematica program deleted by N. J. A. Sloane, Jul 08 2009

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