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 A110601 a(n) = phi(n)*tau(n)^2, where phi is Euler's totient function and tau(n) is the number of divisors of n. 2

%I

%S 1,4,8,18,16,32,24,64,54,64,40,144,48,96,128,200,64,216,72,288,192,

%T 160,88,512,180,192,288,432,112,512,120,576,320,256,384,972,144,288,

%U 384,1024,160,768,168,720,864,352,184,1600,378,720,512,864,208,1152,640

%N a(n) = phi(n)*tau(n)^2, where phi is Euler's totient function and tau(n) is the number of divisors of n.

%H Vincenzo Librandi, <a href="/A110601/b110601.txt">Table of n, a(n) for n = 1..2000</a>

%H S. Porubsky and M. G. Greening, <a href="http://www.jstor.org/stable/2319097">Problem E2351</a>, Amer. Math. Monthly, 80, 1973, p. 436.

%e a(4)=18 because phi(4)=2 and tau(4)=3.

%p with(numtheory): a:=n->phi(n)*tau(n)^2: seq(a(n),n=1..70);

%t Table[EulerPhi[n]DivisorSigma[0,n]^2,{n,60}] (* _Harvey P. Dale_, Nov 29 2011 *)

%o (PARI) a(n) = eulerphi(n)*numdiv(n)^2; \\ _Michel Marcus_, Jun 21 2017

%o (MAGMA) [EulerPhi(n)*NumberOfDivisors(n)^2: n in [1..60]]; // _Vincenzo Librandi_, Jun 21 2017

%Y Cf. A062355, A035116.

%K nonn,mult

%O 1,2

%A _Emeric Deutsch_, Jul 29 2005

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Last modified July 29 16:52 EDT 2021. Contains 346346 sequences. (Running on oeis4.)