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

1,1

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}.

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: A247549 A140154 A350997 * A322952 A101966 A341423

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