OFFSET
1,2
COMMENTS
See A066272 for definition of anti-divisor.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..1000
EXAMPLE
30 is here since it has three distinct primes that divide it: {2, 3, 5} and three anti-divisors: {4, 12, 20}.
MATHEMATICA
atd[n_] := Count[Flatten[Quotient[#, Rest[Select[Divisors[#], OddQ]]] & /@ (2 n + Range[-1, 1])], Except[1]]; Select[Range[9030], PrimeNu[#] == atd[#] &] (* Jayanta Basu, Jul 08 2013 *)
PROG
(PARI) {for(n=1, 9050, 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]==matsize(factor(n))[1], print1(n, ", ")))}
(Python3)
from sympy import divisors, factorint
A073713 = [n for n in range(1, 10**5) if len(factorint(n)) == len([2*d for d in divisors(n) if n > 2*d and n % (2*d)] + [d for d in divisors(2*n-1) if n > d >= 2 and n % d] + [d for d in divisors(2*n+1) if n > d >= 2 and n % d])] # Chai Wah Wu, Aug 13 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Aug 30 2002
EXTENSIONS
Edited and extended by Klaus Brockhaus, Sep 02 2002
STATUS
approved