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A143610 Numbers of the form p^2*q^3, where p,q are distinct primes. 15
72, 108, 200, 392, 500, 675, 968, 1125, 1323, 1352, 1372, 2312, 2888, 3087, 3267, 4232, 4563, 5324, 6125, 6728, 7688, 7803, 8575, 8788, 9747, 10952, 11979, 13448, 14283, 14792, 15125, 17672, 19652, 19773, 21125, 22472, 22707, 25947, 27436 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also: numbers with prime signature {3,2}.

This is a subsequence of A114128. [Hasler]

Every a(n) is an Achilles number (A052486). They are minimal, meaning no proper divisor is an Achilles number. [Antonio Roldán, Dec 27 2011]

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Project Euler, Problem 200.

Index to sequences related to prime signature

EXAMPLE

The first elements of this sequence are 3^2*2^3 = 72, 2^2*3^3 = 108, 5^2*2^3 = 200.

MATHEMATICA

f[n_] := Sort[Last/@FactorInteger[n]] == {2, 3}; Select[Range[30000], f] (* Vladimir Joseph Stephan Orlovsky, Oct 09 2009 *)

PROG

(PARI) for(n=1, 10^5, omega(n)==2|next; vecsort(factor(n)[, 2])==[2, 3]~ & print1(n", ")) \\ Hasler

(PARI) list(lim)=my(v=List(), t); forprime(p=2, (lim\4)^(1/3), t=p^3; forprime(q=2, sqrt(lim\t), if(p==q, next); listput(v, t*q^2))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011

CROSSREFS

Cf. A114128.

Sequence in context: A072412 A052486 A114128 * A166987 A251124 A169644

Adjacent sequences:  A143607 A143608 A143609 * A143611 A143612 A143613

KEYWORD

easy,nonn,changed

AUTHOR

M. F. Hasler, Aug 27 2008

STATUS

approved

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Last modified May 29 21:28 EDT 2017. Contains 287257 sequences.