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A245497 a(n) = phi(n)^2/2, where phi(n) = A000010(n), the Euler totient function. 2

%I

%S 2,2,8,2,18,8,18,8,50,8,72,18,32,32,128,18,162,32,72,50,242,32,200,72,

%T 162,72,392,32,450,128,200,128,288,72,648,162,288,128,800,72,882,200,

%U 288,242,1058,128,882,200,512,288,1352,162,800,288,648,392,1682

%N a(n) = phi(n)^2/2, where phi(n) = A000010(n), the Euler totient function.

%C Values of a(n) < 3 are non-integers since phi(1) = phi(2) = 1 (odd). Since phi(n) is even for all n > 2, a(n) is a positive integer.

%C a(n) gives the sum of all the parts in the partitions of phi(n) with exactly two parts (see example).

%C a(n) is also the area of a square with diagonal phi(n).

%H Jens Kruse Andersen, <a href="/A245497/b245497.txt">Table of n, a(n) for n = 3..10000</a>

%F a(n) = phi(n)^2/2 = A000010(n)^2/2 = A127473(n)/2, n > 2.

%e a(5) = 8; since phi(5)^2/2 = 4^2/2 = 8. The partitions of phi(5) = 4 into exactly two parts are: (3,1) and (2,2). The sum of all the parts in these partitions gives: 3+1+2+2 = 8.

%e a(7) = 18; since phi(7)^2/2 = 6^2/2 = 18. The partitions of phi(7) = 6 into exactly two parts are: (5,1), (4,2) and (3,3). The sum of all the parts in these partitions gives: 5+1+4+2+3+3 = 18.

%p with(numtheory): 245497:=n->phi(n)^2/2: seq(245497(n), n=3..50);

%t Table[EulerPhi[n]^2/2, {n, 3, 50}]

%o (PARI) vector(100, n, eulerphi(n+2)^2/2) \\ _Derek Orr_, Aug 04 2014

%Y Cf. A000010, A127473.

%K nonn,easy

%O 3,1

%A _Wesley Ivan Hurt_, Jul 24 2014

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Last modified January 17 09:54 EST 2020. Contains 330949 sequences. (Running on oeis4.)