cp's OEIS Frontend

A355446 Numbers of the form p^2 * q where p and q are primes with p < q < p^2.

%I A355446 #21 May 28 2025 09:16:36
%S A355446 12,45,63,175,275,325,425,475,539,575,637,833,931,1127,1421,1519,1573,
%T A355446 1813,2009,2057,2107,2299,2303,2783,2873,3211,3509,3751,3887,4477,
%U A355446 4901,4961,5203,5239,5491,5687,6253,6413,6647,6929,7139,7267,7381,7943,8107,8303,8381,8591,8833,8957,8959,9559,9971,10043,10309,10469
%N A355446 Numbers of the form p^2 * q where p and q are primes with p < q < p^2.
%C A355446 Numbers whose number of divisors of n (A000005) is equal to 3 + the number of prime factors of n (with multiplicity, A001222), and the fourth smallest divisor is a square of a prime (A001248).
%e A355446 12 = 2^2 * 3 is included because 2 < 3, and of the divisors of 12, [1, 2, 3, 4, 6, 12], the fourth one (4) is a square of prime as 2^2 > 3.
%t A355446 Select[Range[10^4], (f = FactorInteger[#])[[;; , 2]] == {2, 1} && f[[1, 1]]^2 > f[[2, 1]] &] (* _Amiram Eldar_, Jul 07 2022 *)
%o A355446 (PARI)
%o A355446 A355444(n) = ((numdiv(n) == (3+bigomega(n))) && issquare(divisors(n)[4]));
%o A355446 isA355446(n) = A355444(n);
%Y A355446 Setwise difference A096156 \ A355445.
%Y A355446 Positions of 6's in A290110 and in A300250.
%Y A355446 Subsequence of A066680, and of A355455.
%Y A355446 A251720 is a subsequence.
%Y A355446 Cf. A000005, A001222, A001248, A355444 (characteristic function).
%K A355446 nonn
%O A355446 1,1
%A A355446 _Antti Karttunen_, Jul 02 2022