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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.

%I A110601 #23 Dec 29 2022 06:31:17
%S A110601 1,4,8,18,16,32,24,64,54,64,40,144,48,96,128,200,64,216,72,288,192,
%T A110601 160,88,512,180,192,288,432,112,512,120,576,320,256,384,972,144,288,
%U A110601 384,1024,160,768,168,720,864,352,184,1600,378,720,512,864,208,1152,640
%N 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.
%H A110601 Vincenzo Librandi, <a href="/A110601/b110601.txt">Table of n, a(n) for n = 1..2000</a>
%H A110601 Stefan Porubsky and M. G. Greening, <a href="http://www.jstor.org/stable/2319097">Problem E2351</a>, Amer. Math. Monthly, Vol. 80, No. 4 (1973), p. 436.
%F A110601 a(n) = A000010(n) * A035116(n) = A062355(n) * A000005(n). - _R. J. Mathar_, Jul 26 2022
%F A110601 Multiplicative with a(p^e) = (e+1)^2*(p-1)*p^(e-1). - _Amiram Eldar_, Dec 29 2022
%e A110601 a(4)=18 because phi(4)=2 and tau(4)=3.
%p A110601 with(numtheory): a:=n->phi(n)*tau(n)^2: seq(a(n),n=1..70);
%t A110601 Table[EulerPhi[n]DivisorSigma[0,n]^2,{n,60}] (* _Harvey P. Dale_, Nov 29 2011 *)
%o A110601 (PARI) a(n) = eulerphi(n)*numdiv(n)^2; \\ _Michel Marcus_, Jun 21 2017
%o A110601 (Magma) [EulerPhi(n)*NumberOfDivisors(n)^2: n in [1..60]]; // _Vincenzo Librandi_, Jun 21 2017
%Y A110601 Cf. A000005, A000010, A035116, A062355.
%K A110601 nonn,mult
%O A110601 1,2
%A A110601 _Emeric Deutsch_, Jul 29 2005