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

12, 45, 63, 175, 275, 325, 425, 475, 539, 575, 637, 833, 931, 1127, 1421, 1519, 1573, 1813, 2009, 2057, 2107, 2299, 2303, 2783, 2873, 3211, 3509, 3751, 3887, 4477, 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

Offset: 1

Author

Antti Karttunen, Jul 02 2022

Keywords

• nonn

Comments

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).

Examples

			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.
		

Crossrefs

Setwise difference A096156 \ A355445.

Positions of 6's in A290110 and in A300250.

Subsequence of A066680, and of A355455.

A251720 is a subsequence.

Cf. A000005, A001222, A001248, A355444 (characteristic function).

Programs

Mathematica

Select[Range[10^4], (f = FactorInteger[#])[[;; , 2]] == {2, 1} && f[[1, 1]]^2 > f[[2, 1]] &] (* Amiram Eldar, Jul 07 2022 *)

PARI

A355444(n) = ((numdiv(n) == (3+bigomega(n))) && issquare(divisors(n)[4]));
isA355446(n) = A355444(n);