A355445 Numbers of the form p^2 * q where p and q are primes with p^2 < q.

20, 28, 44, 52, 68, 76, 92, 99, 116, 117, 124, 148, 153, 164, 171, 172, 188, 207, 212, 236, 244, 261, 268, 279, 284, 292, 316, 332, 333, 356, 369, 387, 388, 404, 412, 423, 428, 436, 452, 477, 508, 524, 531, 548, 549, 556, 596, 603, 604, 628, 639, 652, 657, 668, 692, 711, 716, 724, 725, 747, 764, 772, 775, 788, 796

Offset

1,1

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 third smallest divisor is a square of a prime (A001248).

Links

Table of n, a(n) for n=1..65.

Example

20 = 2^2 * 5 is included because 2 < 5, and of the divisors of 20, [1, 2, 4, 5, 10, 20], the third one (4) is a square of prime as 2^2 < 5.

Mathematica

Select[Range[800], (f = FactorInteger[#])[[;; , 2]] == {2, 1} && f[[1, 1]]^2 < f[[2, 1]] &] (* Amiram Eldar, Jul 07 2022 *)

Prog

(PARI)
A355443(n) = ((numdiv(n) == (3+bigomega(n))) && issquare(divisors(n)[3]));
isA355445(n) = A355443(n);

Crossrefs

Setwise difference A096156 \ A355446. Subsequence of A119315.

Positions of 9's in A290110 and in A300250.

Cf. A000005, A001222, A001248, A355443 (characteristic function).

Sequence in context: A309780 A139703 A317924 * A145567 A344795 A043109

Adjacent sequences: A355442 A355443 A355444 * A355446 A355447 A355448

Keyword

nonn

Author

Antti Karttunen, Jul 02 2022

Status

approved