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A211781 Numbers n such that Sum_(d_<n | n) tau(d_<n) / (d_<n) is integer, where d_<n = divisors of n that are less than n, tau(x) = A000005(x). 1
2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 27, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 225, 227, 229, 233, 239, 241, 251, 252 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Union primes (A000040) and sequence of composite numbers: 4, 27, 225, 252, 672, 1200, ...

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

Number 225 is in sequence because 1/1 + 2/3 + 2/5 + 3/9 + 4/15 + 3/25 + 6/45 + 6/75 = 3 (integer).

MAPLE

with(numtheory);

A211781:= proc(q)

local b, d, j, n;

for n from 2 to q do

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

  if trunc(d)=d then print(n); fi;

od; end:

A211781(10000); # Paolo P. Lava, Feb 01 2013

MATHEMATICA

t = {}; Do[d2 = Sum[DivisorSigma[0, d]/d, {d, Most[Divisors[n]]}]; If[IntegerQ[d2], AppendTo[t, n]], {n, 2, 252}]; t (* T. D. Noe, Apr 26 2012 *)

CROSSREFS

Sequence in context: A036844 A284696 A033070 * A046022 A175787 A073019

Adjacent sequences:  A211778 A211779 A211780 * A211782 A211783 A211784

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Apr 20 2012

STATUS

approved

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Last modified September 26 02:39 EDT 2020. Contains 337346 sequences. (Running on oeis4.)