

A096156


Numbers with ordered prime signature (2,1).


5



12, 20, 28, 44, 45, 52, 63, 68, 76, 92, 99, 116, 117, 124, 148, 153, 164, 171, 172, 175, 188, 207, 212, 236, 244, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 356, 369, 387, 388, 404, 412, 423, 425, 428, 436, 452, 475, 477, 508, 524, 531, 539, 548, 549
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OFFSET

1,1


COMMENTS

Numbers of the form p^2 * q where p and q are primes with p < q.
Also a(n) = the members of A054753 that are not in A095990.
There are pairs that differ by 1, which is not the case in A095990, beginning with 44 and 45, 116 and 117, 171 and 172, 332 and 333, etc.


LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
OEIS Wiki, Ordered prime signatures


EXAMPLE

a(2) = 20 because 20 = 2*2*5 and 2 < 5.
Note that 18 = 2*3^2 is not in the sequence, even though it has prime signature (2,1), because its ordered prime signature is (1,2) (A095990). Prime signatures correspond to partitions of Omega(n), while ordered prime signatures correspond to compositions of Omega(n).


MATHEMATICA

Take[ Sort[ Flatten[ Table[ Prime[p]^2 Prime[q], {q, 2, 33}, {p, q  1}]]], 54] (* Robert G. Wilson v, Jul 28 2004 *)
Select[Range[10^5], FactorInteger[#][[All, 2]]=={2, 1}&] (* Enrique Pérez Herrero, Jun 27 2012 *)


PROG

(PARI) list(lim)=my(v=List()); forprime(q=3, lim\4, forprime(p=2, min(sqrtint(lim\q), q1), listput(v, p^2*q))); Set(v) \\ Charles R Greathouse IV, Feb 26 2014


CROSSREFS

Cf. A095990, A054753.
Sequence in context: A090767 A117227 A110187 * A210968 A107277 A256883
Adjacent sequences: A096153 A096154 A096155 * A096157 A096158 A096159


KEYWORD

nonn,easy


AUTHOR

Alford Arnold, Jul 24 2004


EXTENSIONS

Edited and extended by Robert G. Wilson v and Rick L. Shepherd, Jul 27 2004


STATUS

approved



