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).

1, 2, 6, 8, 12, 15, 24, 28, 30, 40, 70, 84, 112, 120, 140, 210, 240, 252, 280, 315, 336, 351, 357, 360, 420, 550, 630, 684, 702, 714, 836, 840, 884, 912, 952, 988, 1092, 1100, 1120, 1140, 1364, 1386, 1650, 1710, 1820, 2002, 2040, 2088, 2090, 2200, 2394, 2484

Offset: 1

Author

Michel Lagneau, Jan 28 2016

Keywords

• nonn

Comments

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,...

A majority of numbers of the sequence are even, except 1, 15, 315, 351, 357, 2871, 3663,...

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002322.

Programs

Mathematica

lst={};Do[If[IntegerQ[Total[1/CarmichaelLambda[Divisors[n]]]],AppendTo[lst,n]], {n, 0, 2500}];lst