A211778 Composite numbers n such that Sum_{d_<n | n} phi(d_<n) / (d_<n) is an integer, where d_<n = divisors of n that are less than n, phi(x) = A000010(x).

8, 12, 32, 80, 81, 128, 189, 196, 324, 336, 448, 512, 576, 768, 1600, 1936, 2025, 2048, 2187, 2500, 5292, 5324, 5616, 5780, 8192, 8748, 9477, 11264, 12096, 13520, 14400, 14800, 15552, 15625, 20736, 32768, 35721, 36864, 49152, 53248, 59049, 69696, 73575, 73872

Offset

1,1

Comments

Complement of primes (A000040) with respect to A211777.

Links

Table of n, a(n) for n=1..44.

Example

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

Mathematica

t = {}; Do[If[! PrimeQ[n], d2 = Sum[EulerPhi[d]/d, {d, Most[Divisors[n]]}]; If[IntegerQ[d2], AppendTo[t, n]]], {n, 2, 10000}]; t (* T. D. Noe, Apr 26 2012 *)

Prog

(PARI) is(n)=denominator(sumdiv(n, d, if(d<n, eulerphi(d)/d)))==1 && !isprime(n) \\ Charles R Greathouse IV, Mar 05 2013

Crossrefs

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

Sequence in context: A217156 A066934 A137148 * A045018 A067681 A132356

Adjacent sequences: A211775 A211776 A211777 * A211779 A211780 A211781

Keyword

nonn,changed

Author

Jaroslav Krizek, Apr 20 2012

Extensions

Extended by T. D. Noe, Apr 26 2012

Status

approved