OFFSET
1,1
COMMENTS
Numbers of the form m * p^2 * q^2, where p < q are primes, and m is a squarefree number such that gcd(m, p*q) = 1.
The asymptotic density of this sequence is ((Sum_{p prime} 1/(p*(p+1)))^2 - Sum_{p prime} 1/(p*(p+1))^2)/(2*zeta(2)) = 0.022124574473271163980012... .
LINKS
EXAMPLE
36 = 2^2 * 3^2 is a term since its prime factorization has exactly two exponents and both are equal to 2.
MATHEMATICA
q[n_] := Module[{e = Sort[FactorInteger[n][[;; , 2]], Greater]}, Length[e] > 1 && e[[1;; 2]] == {2, 2} && If[Length[e] > 2, e[[3]] == 1, True]]; Select[Range[2200], q]
PROG
(PARI) is(k) = {my(e = vecsort(factor(k)[, 2], , 4)~); #e > 1 && e[1..2] == [2, 2] && if(#e > 2, e[3] == 1, 1); }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 01 2024
STATUS
approved