A073694 Numbers k such that the number of divisors of k equals the number of anti-divisors of k.
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
Offset: 1
Keywords
Examples
32 is here since it has 6 divisors: {1, 2, 4, 8, 16, 32} and 6 anti-divisors: {3, 5, 7, 9, 13, 21}.
Links
- Vincenzo Librandi and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 227 terms from Vincenzo Librandi)
Programs
-
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 *)
-
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,",")))}
Extensions
Edited and extended by Klaus Brockhaus, Sep 01 2002
Comments