login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Half-totient function of n is divisible by the number of divisors of n.
0

%I #8 Feb 06 2019 18:34:22

%S 5,9,13,15,17,28,29,34,35,37,39,40,41,45,49,51,52,53,55,61,63,65,72,

%T 73,76,82,84,85,87,89,90,91,95,97,99,101,102,104,105,109,111,113,115,

%U 117,119,120,123,124,128,130,136,137,140,143,145,146,147,148,149,153,155

%N Half-totient function of n is divisible by the number of divisors of n.

%C Half-totient function is phi(n)/2 for n >= 3, A023022.

%t Select[Range[200],Divisible[EulerPhi[#]/2,DivisorSigma[0,#]]&] (* _Harvey P. Dale_, Feb 06 2019 *)

%o (PARI) j=[]; for(n=3,350, if(Mod(eulerphi(n)/2,numdiv(n))==0,j=concat(j,n))); j

%Y Cf. A023022.

%K nonn

%O 3,1

%A _Jason Earls_, Jul 24 2001