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

1,2

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000010, A002322.

Sequence in context: A282358 A064796 A304483 * A083769 A057656 A247066

Adjacent sequences: A268174 A268175 A268176 * A268178 A268179 A268180

Keyword

nonn

Author

Michel Lagneau, Jan 28 2016

Status

approved