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 A143610 Numbers of the form p^2 * q^3, where p,q are distinct primes. 21
 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: Find the 200th prime-proof sqube containing the contiguous sub-string 200. Index to sequences related to prime signature FORMULA Sum_{n>=1} 1/a(n) = P(2)*P(3) - P(5) = A085548 * A085541 - A085965 = 0.043280..., where P is the prime zeta function. - Amiram Eldar, Jul 06 2020 EXAMPLE The first three terms 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", ")) (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. Cf. A085541, A085548, A085965. Sequence in context: A072412 A052486 A114128 * A166987 A339940 A251124 Adjacent sequences: A143607 A143608 A143609 * A143611 A143612 A143613 KEYWORD easy,nonn AUTHOR M. F. Hasler, Aug 27 2008 STATUS approved

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Last modified May 29 10:54 EDT 2024. Contains 372938 sequences. (Running on oeis4.)