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A053820 Sum_{k=1..n, gcd(n,k) = 1} k^4. 2

%I

%S 1,1,17,82,354,626,2275,3108,7395,9044,25333,17668,60710,50470,88388,

%T 103496,243848,129750,432345,266088,497574,497178,1151403,539912,

%U 1541770,1153724,1900089,1516844,3756718,1246568,5273999

%N Sum_{k=1..n, gcd(n,k) = 1} k^4.

%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 48, problem 15, the function phi_4(n).

%D L. E. Dickson, History of the Theory of Numbers, Vol. I (Reprint 1966), p. 140.

%H Vincenzo Librandi, <a href="/A053820/b053820.txt">Table of n, a(n) for n = 1..1000</a>

%H P. G. Brown, <a href="http://www.jstor.org/stable/3621931">Some comments on inverse arithmetic functions</a>, Math. Gaz. 89 (2005) 403-408.

%F a(n)=(6*n^4*A000010(n)+10*n^3*A023900(n)-n*A063453(n))/30 for n>1. Formula is derived from a more general formula of A. Thacker (1850), see [Dickson, Brown]. - _Franz Vrabec_, Aug 21 2005

%t a[n_] := Sum[If[GCD[n, k] == 1, k^4, 0], {k, 1, n}]; Table[a[n], {n, 1, 31}] (* _Jean-Fran├žois Alcover_, Feb 26 2014 *)

%o (PARI) a(n) = sum(k=1, n, (gcd(n,k) == 1)*k^4); \\ _Michel Marcus_, Feb 26 2014

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Apr 07 2000

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Last modified October 31 03:51 EDT 2014. Contains 248845 sequences.