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A248007 Least positive integer m such that m + n divides phi(m)*phi(n), where phi(.) is Euler's totient function. 8

%I

%S 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 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 15,26,28,36,35,28,9,64,7,54,21,28,19,26

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

%C Conjecture: a(n) exists for any n > 6. - _Zhi-Wei Sun_, Sep 29 2014

%C 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 a(2^n) <= 2^n for all n > 2. Also, if a(i) = j, then a(j) <= i. - _Derek Orr_, Sep 29 2014

%H Zhi-Wei Sun, <a href="/A248007/b248007.txt">Table of n, a(n) for n = 7..10000</a>

%e a(10) = 14 since 10 + 14 divides phi(10)*phi(14) = 4*6 = 24.

%t 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 (PARI)

%o a(n)=m=1;while((eulerphi(m)*eulerphi(n))%(m+n),m++);m

%o vector(100,n,a(n+6)) \\ _Derek Orr_, Sep 29 2014

%Y Cf. A000010, A248004, A248006, A248008.

%K nonn

%O 7,1

%A _Zhi-Wei Sun_, Sep 29 2014

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Last modified January 23 17:33 EST 2022. Contains 350514 sequences. (Running on oeis4.)