A211777 Numbers n such that Sum_{d_<n | n} phi(d_<n) / (d_<n) is integer, where d_<n = divisors of n that are less than n, phi(x) = A000010(x).

2, 3, 5, 7, 8, 11, 12, 13, 17, 19, 23, 29, 31, 32, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 80, 81, 83, 89, 97, 101, 103, 107, 109, 113, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 189, 191, 193, 196, 197, 199, 211, 223, 227, 229, 233

Offset

1,1

Comments

Union primes (A000040) and A211778.

Links

Table of n, a(n) for n=1..59.

Example

For n = 32 holds: 1/1 + 1/2 + 2/4 + 4/8 + 8/16 = 3 (integer).

Mathematica

t = {}; Do[d2 = Sum[EulerPhi[d]/d, {d, Most[Divisors[n]]}]; If[IntegerQ[d2], AppendTo[t, n]], {n, 2, 233}]; t (* T. D. Noe, Apr 26 2012 *)

Prog

(PARI) is(n)=denominator(sumdiv(n, d, if(d<n, eulerphi(d)/d)))==1 \\ Charles R Greathouse IV, Feb 21 2013

Crossrefs

Cf: A066862 (numbers n such that Sum_{d | n} phi(d) / d is integer).

Sequence in context: A346635 A359159 A298865 * A189299 A028780 A284655

Adjacent sequences: A211774 A211775 A211776 * A211778 A211779 A211780

Keyword

nonn

Author

Jaroslav Krizek, Apr 20 2012

Status

approved