A073694 - OEIS

%I #24 Feb 20 2024 06:59:44

%S 5,32,50,162,512,1984,2450,3784,5408,7564,9248,15488,19208,22684,

%T 26680,30752,53792,79600,85698,102604,113764,131584,189112,199712,

%U 279752,336200,435244,514098,546012,581042,658952,712818,727218,752764,767560

%N Numbers k such that the number of divisors of k equals the number of anti-divisors of k.

%C See A066272 for definition of anti-divisor.

%H Vincenzo Librandi and Donovan Johnson, <a href="/A073694/b073694.txt">Table of n, a(n) for n = 1..1000</a> (first 227 terms from Vincenzo Librandi)

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

%t 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 *)

%o (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,",")))}

%Y Cf. A000005, A066272.

%K nonn

%O 1,1

%A _Jason Earls_, Aug 30 2002

%E Edited and extended by _Klaus Brockhaus_, Sep 01 2002