cp's OEIS Frontend

A377121 Numbers whose totient is refactorable.

%I A377121 #17 Dec 12 2024 18:24:19
%S A377121 1,2,3,4,6,13,15,16,19,20,21,24,26,27,28,30,35,36,37,38,39,41,42,45,
%T A377121 52,54,55,56,57,61,63,70,72,73,74,75,76,77,78,82,84,87,88,89,90,91,93,
%U A377121 95,97,99,100,108,109,110,111,114,115,116,117,119,122,123,124,126,129,132,133,135,137,146,147,148,150,152,153
%N A377121 Numbers whose totient is refactorable.
%C A377121 If k is an odd term, 2*k is also a term due to the multiplicative nature of the totient function and their totients are equal.
%H A377121 Robert Israel, <a href="/A377121/b377121.txt">Table of n, a(n) for n = 1..10000</a>
%e A377121 3, 4, and 6 are terms as their totients equal 2, which is the second refactorable number.
%p A377121 filter:= proc(n) local p;
%p A377121   p:= numtheory:-phi(n);
%p A377121   p mod numtheory:-tau(p) = 0
%p A377121 end proc:
%p A377121 select(filter, [$1..200]); # _Robert Israel_, Dec 12 2024
%t A377121 Select[Range[200], Mod[EulerPhi[#], DivisorSigma[0,EulerPhi[#]]]==0&]
%o A377121 (PARI) for(n=1, 200, a=eulerphi(n); a%numdiv(a)==0&&print1(n", "))
%o A377121 (Python)
%o A377121 from sympy import divisor_sigma, totient
%o A377121 for i in range(1, 200):
%o A377121     if totient(i)%divisor_sigma(totient(i), 0)==0:
%o A377121         print(i, end=", ")
%Y A377121 Cf. A000010, A033950.
%K A377121 nonn
%O A377121 1,2
%A A377121 _Waldemar Puszkarz_, Oct 17 2024