A073716 Numbers n such that the number of prime divisors of n (counted with multiplicity) = number of anti-divisors of n.

1, 3, 9, 20, 30, 40, 44, 80, 84, 100, 114, 168, 174, 192, 208, 244, 256, 272, 300, 316, 324, 404, 440, 456, 464, 520, 524, 596, 672, 704, 720, 834, 894, 1044, 1064, 1248, 1272, 1324, 1416, 1464, 1604, 1608, 1626, 1632, 1636, 1680, 1686, 1704, 1744, 1756

Offset

1,2

Comments

See A066272 for definition of anti-divisor.

Links

Table of n, a(n) for n=1..50.

Example

40 is a term since its prime factors are {2, 2, 2, 5} and its anti-divisors are {3, 9, 16, 27}.

Mathematica

atd[n_] := Count[Flatten[Quotient[#, Rest[Select[Divisors[#], OddQ]]] & /@ (2 n + Range[-1, 1])], Except[1]]; Select[Range[1760], PrimeOmega[#] == atd[#] &] (* Jayanta Basu, Jul 08 2013 *)

Prog

(PARI) {for(n=1, 1800, 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]==bigomega(n), print1(n, ", ")))}

Crossrefs

Cf. A001222, A066272.

Sequence in context: A033315 A200612 A355136 * A174866 A187409 A037048

Adjacent sequences: A073713 A073714 A073715 * A073717 A073718 A073719

Keyword

nonn

Author

Jason Earls, Aug 30 2002

Extensions

Edited and extended by Klaus Brockhaus, Sep 02 2002

Status

approved