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A073694 Numbers k such that the number of divisors of k equals the number of anti-divisors of k. 2
5, 32, 50, 162, 512, 1984, 2450, 3784, 5408, 7564, 9248, 15488, 19208, 22684, 26680, 30752, 53792, 79600, 85698, 102604, 113764, 131584, 189112, 199712, 279752, 336200, 435244, 514098, 546012, 581042, 658952, 712818, 727218, 752764, 767560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A066272 for definition of anti-divisor.

LINKS

Vincenzo Librandi and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 227 terms from Vincenzo Librandi)

EXAMPLE

32 is here since it has 6 divisors: {1, 2, 4, 8, 16, 32} and 6 anti-divisors: {3, 5, 7, 9, 13, 21}.

MAPLE

P:=proc(i)

local a, b, k, n;

for n from 3 by 1 to i do

  a:={};

  for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od;

  if tau(n)=nops(a) then print(n); fi;

od;

end:

P(1000000); # Paolo P. Lava, Jun 30 2011

MATHEMATICA

atd[n_] := Count[Flatten[Quotient[#, Rest[Select[Divisors[#], OddQ]]] & /@ (2 n + Range[-1, 1])], Except[1]]; Select[Range[770000], DivisorSigma[0, #] == atd[#] &] (* Jayanta Basu, Jul 06 2013 *)

PROG

(PARI) {for(n=1, 770000, v1=[]; v2=[]; v3=[]; ds=divisors(2*n-1); for(k=2, matsize(ds)[2]-1, if(ds[k]%2>0, v1=concat(v1, ds[k]))); ds=divisors(2*n); for(k=2, matsize(ds)[2]-1, if(ds[k]%2>0, v2=concat(v2, ds[k]))); ds=divisors(2*n+1); for(k=2, matsize(ds)[2]-1, if(ds[k]%2>0, v3=concat(v3, ds[k]))); v=vecsort(concat(v1, concat(v2, v3))); if(matsize(v)[2]==numdiv(n), print1(n, ", ")))}

CROSSREFS

Cf. A000005, A066272.

Sequence in context: A265159 A247549 A140154 * A322952 A101966 A184536

Adjacent sequences:  A073691 A073692 A073693 * A073695 A073696 A073697

KEYWORD

nonn

AUTHOR

Jason Earls, Aug 30 2002

EXTENSIONS

Edited and extended by Klaus Brockhaus, Sep 01 2002

STATUS

approved

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)