login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; graph; refs; listen; history; text; internal format)
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).

MAPLE

with(numtheory);

A211777:= proc(q)

local b, d, j, n;

for n from 2 to q do

  b:=divisors(n); d:=add(phi(b[j])/b[j], j=1..nops(b))-phi(n)/n;

  if trunc(d)=d then print(n); fi;

od; end:

A211777(10000); # Paolo P. Lava, Feb 01 2013

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: A141832 A066680 A298865 * A189299 A028780 A284655

Adjacent sequences:  A211774 A211775 A211776 * A211778 A211779 A211780

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Apr 20 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 17:07 EST 2019. Contains 319350 sequences. (Running on oeis4.)