Search: id:A001065
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%I A001065 M2226 N0884
%S A001065 0,1,1,3,1,6,1,7,4,8,1,16,1,10,9,15,1,21,1,22,11,14,1,36,6,16,13,28,1,
%T A001065 42,1,31,15,20,13,55,1,22,17,50,1,54,1,40,33,26,1,76,8,43,21,46,1,66,17,
%U A001065 64,23,32,1,108,1,34,41,63,19,78,1,58,27,74,1,123,1,40,49,64,19,90,1,106
%N A001065 Sum of proper divisors (or aliquot parts) of n: sum of divisors of n
that are less than n.
%C A001065 Equals row sums of triangle A141846 - Gary W. Adamson (qntmpkt(AT)yahoo.com),
Jul 11 2008
%D A001065 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences,
Academic Press, 1995 (includes this sequence).
%D A001065 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973
(includes this sequence).
%D A001065 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions,
National Bureau of Standards Applied Math. Series 55, 1964 (and various
reprintings), p. 840.
%D A001065 George E. Andrews, Number Theory. New York: Dover, 1994 . Pages 1, 75-92;
p. 92 #15: Sigma(n) / d(n) >= n^(1/2).
%H A001065 T. D. Noe, Table of n, a(n) for n = 1..10000
%H A001065 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National
Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972
[alternative scanned copy].
%H A001065 H. Bottomley, Illustration of initial terms
%H A001065 Primefan,
Sums of Restricted Divisors for n=1 to 1000
%H A001065 F. Richman,
Aliquot series:Abundant,deficient,perfect
%H A001065 Eric Weisstein's World of Mathematics, Link to a section of The World of
Mathematics (1).
%H A001065 Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
(2).
%H A001065 Index entries for "core" sequences
%F A001065 G.f.: Sum_{k>0} k x^(2k)/(1-x^k) - Michael Somos Jul 05 2006
%F A001065 a(n) = sigma(n) - n = A000203(n) - n. - Lekraj Beedassy (blekraj(AT)yahoo.com),
Jun 02 2005
%F A001065 Equals inverse Mobius transform of A051953 = A051731 * A051953. Example:
a(6) = 6 = (1, 1, 1, 0, 0, 1) dot (0, 1, 1, 2, 1, 4) = (0 + 1 + 1
+ 0 + 0 + 4), where A051953 = (0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8,
...) and (1, 1, 1, 0, 0, 1) = row 6 of A051731 where the 1's positions
indicate the factors of 6. - Gary W. Adamson (qntmpkt(AT)yahoo.com),
Jul 11 2008
%e A001065 For n=44, sum of divisors of n = sigma(n) = 84; so a(44) = 84-44 = 40.
%p A001065 with(numtheory); [ seq(sigma(n)-n,n=1..100) ];
%t A001065 Table[ Plus @@ Select[ Divisors[ n ], #