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%I #12 Feb 14 2024 16:02:42
%S 2,12,4,2,3,6,2,10,3,2,21,8,3,22,13,8,9,6,8,12,3,8,10,4,5,10,21,8,20,
%T 26,4,8,7,14,13,12,8,4,33,8,23,6,20,12,3,16,22,72,7,10,13,4,27,42,5,
%U 24,15,26,57,18,11,38,27,20,31,4,21,36,19,2
%N Least positive integer m such that m + n divides sigma(m)*phi(n), where sigma(.) and phi(.) are given by A000203 and A000010.
%C Conjecture: a(n) < 2*n for any n > 2.
%C Numbers n such that a(n) > n: 1, 2, 3, 8, 11, 14, 48, 227, 908, 4478, ... The next number, if it exists, is greater than 10^5. - _Derek Orr_, Sep 29 2014
%H Zhi-Wei Sun, <a href="/A248030/b248030.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 12 since 12 + 2 = 14 divides sigma(12)*phi(2) = 28.
%t Do[m=1;Label[aa];If[Mod[DivisorSigma[1,m]*EulerPhi[n],m+n]==0,Print[n," ",m];Goto[bb]];m= m+1; Goto[aa];Label[bb];Continue,{n,1,70}]
%t lpim[n_]:=Module[{m=1,ephn=EulerPhi[n]},While[Mod[ephn*DivisorSigma[1,m],m+n]!=0, m++]; m]; Array[lpim,70] (* _Harvey P. Dale_, Feb 14 2024 *)
%o (PARI)
%o a(n)=m=1;while((eulerphi(n)*sigma(m))%(m+n),m++);m
%o vector(100,n,a(n)) \\ _Derek Orr_, Sep 29 2014
%Y Cf. A000010, A000203, A248004, A248007, A248008, A248029.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Sep 29 2014
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