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A268177 Numbers m such that Sum_{i=1..q} 1/lambda(d(i)) is an integer, where d(i) are the q divisors of m and lambda is the Carmichael lambda function (A002322).

%I A268177 #9 Jul 13 2019 09:16:55
%S A268177 1,2,6,8,12,15,24,28,30,40,70,84,112,120,140,210,240,252,280,315,336,
%T A268177 351,357,360,420,550,630,684,702,714,836,840,884,912,952,988,1092,
%U A268177 1100,1120,1140,1364,1386,1650,1710,1820,2002,2040,2088,2090,2200,2394,2484
%N A268177 Numbers m such that Sum_{i=1..q} 1/lambda(d(i)) is an integer, where d(i) are the q divisors of m and lambda is the Carmichael lambda function (A002322).
%C A268177 The corresponding integers are 1, 2, 3, 3, 4, 2, 5, 3, 4, 4, 3, 5, 4, 7, 4, 5, 8, 6, 5, 3, 7, 2, 2, 8, 7,...
%C A268177 A majority of numbers of the sequence are even, except 1, 15, 315, 351, 357, 2871, 3663,...
%C A268177 Replacing the function lambda(n) by the Euler totient function phi(n) (A000010) gives only the short sequence {1, 2, 6} for n < 10^7.
%H A268177 Amiram Eldar, <a href="/A268177/b268177.txt">Table of n, a(n) for n = 1..10000</a>
%e A268177 6 is in the sequence because the divisors of 6 are {1,2,3,6} => 1/lambda(1)+1/lambda(2)+1/lambda(3)+ 1/lambda(6) = 1/1 + 1/1 + 1/2 + 1/2 = 3 is an integer.
%t A268177 lst={};Do[If[IntegerQ[Total[1/CarmichaelLambda[Divisors[n]]]],AppendTo[lst,n]], {n, 0, 2500}];lst
%Y A268177 Cf. A000010, A002322.
%K A268177 nonn
%O A268177 1,2
%A A268177 _Michel Lagneau_, Jan 28 2016