cp's OEIS Frontend

A248007 Least positive integer m such that m + n divides phi(m)*phi(n), where phi(.) is Euler's totient function.

%I A248007 #14 Sep 29 2014 11:19:54
%S A248007 5,8,3,14,9,20,11,10,9,16,7,18,5,12,3,38,21,8,15,58,9,20,11,18,14,32,
%T A248007 7,14,13,12,35,22,9,24,7,46,13,31,3,42,45,16,11,30,13,44,19,27,25,40,
%U A248007 15,26,28,36,35,28,9,64,7,54,21,28,19,26
%N A248007 Least positive integer m such that m + n divides phi(m)*phi(n), where phi(.) is Euler's totient function.
%C A248007 Conjecture: a(n) exists for any n > 6. - _Zhi-Wei Sun_, Sep 29 2014
%C A248007 Numbers n for which a(n) > n: 10, 12, 22, 26, 42, 78, 166, 266, 290. The next term in this mini-sequence, if it exists, is greater than 3*10^4. I conjecture this list is finite. - _Derek Orr_, Sep 29 2014
%C A248007 a(2^n) <= 2^n for all n > 2. Also, if a(i) = j, then a(j) <= i. - _Derek Orr_, Sep 29 2014
%H A248007 Zhi-Wei Sun, <a href="/A248007/b248007.txt">Table of n, a(n) for n = 7..10000</a>
%e A248007 a(10) = 14 since 10 + 14 divides phi(10)*phi(14) = 4*6 = 24.
%t A248007 Do[m=1; Label[aa]; If[Mod[EulerPhi[m]*EulerPhi[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 7, 70}]
%o A248007 (PARI)
%o A248007 a(n)=m=1;while((eulerphi(m)*eulerphi(n))%(m+n),m++);m
%o A248007 vector(100,n,a(n+6)) \\ _Derek Orr_, Sep 29 2014
%Y A248007 Cf. A000010, A248004, A248006, A248008.
%K A248007 nonn
%O A248007 7,1
%A A248007 _Zhi-Wei Sun_, Sep 29 2014