Search: id:A023896
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%I A023896
%S A023896 1,1,3,4,10,6,21,16,27,20,55,24,78,42,60,64,136,54,171,80,126,110,253,
%T A023896 96,250,156,243,168,406,120,465,256,330,272,420,216,666,342,468,320,
%U A023896 820,252,903,440,540,506,1081,384,1029,500,816,624,1378,486,1100,672
%N A023896 Sum of positive integers in reduced residue system modulo n. a(1) = 1 
               by convention.
%C A023896 a(n) = Sum_{1<=k<=n, GCD(k,n)=1} k.
%C A023896 a(n) = n*A023022(n) for n>2.
%C A023896 Equals row sums of triangle A127368 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 27 2008]
%C A023896 Equals row sums of triangle A144734 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 20 2008]
%C A023896 Equals row sums of triangle A144824 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 21 2008]
%D A023896 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 48, problem 16, the function phi_1(n).
%D A023896 D. M. Burton, Elementary Number Theory, p. 171.
%D A023896 Tattersall, J. "Elementary Number Theory in Nine Chapters", Cambridge 
               University Press, 2001, p. 163.
%H A023896 T. D. Noe, <a href="b023896.txt">Table of n, a(n) for n=1..1000</a>
%F A023896 a(n)=n*phi(n)/2 if n>1, a(1)=0.
%F A023896 a(n) = Sum{1 <= k < n, k for GCD(k, n) =1}.
%F A023896 If n = p is a prime, a(p)=T(p-1) where T(k) is the k-th triangular number 
               (A000217). - Robert G. Wilson v, Jul 31 2004
%F A023896 Equals A054521 * [1,2,3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               May 20 2007
%e A023896 a(12) = 1 + 5 + 7 + 11 = 24.
%e A023896 Reduced residue system for 40 = {1,3,7,9,11,13,17,19,21,23,27,29,31,33,
               37,39}. The sum is 320. Average is 20
%t A023896 a[ n_ ]=n/2*EulerPhi[ n ]; a[ 1 ]=0.
%o A023896 (PARI) a(n)=if(n<2,0,n*eulerphi(n)/2)
%Y A023896 Cf. A000010, A000203, A002180, A045545, A001783, A024816, A066760.
%Y A023896 Cf. A054521.
%Y A023896 A127368 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 27 2008]
%Y A023896 A144734 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2008]
%Y A023896 A144824 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 21 2008]
%Y A023896 Sequence in context: A014411 A143443 A139556 this_sequence A128488 A117781 
               A075100
%Y A023896 Adjacent sequences: A023893 A023894 A023895 this_sequence A023897 A023898 
               A023899
%K A023896 nonn,easy,nice
%O A023896 1,3
%A A023896 Olivier Gerard (olivier.gerard(AT)gmail.com)

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