

A046388


Odd numbers of the form p*q where p and q are distinct primes.


42



15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111, 115, 119, 123, 129, 133, 141, 143, 145, 155, 159, 161, 177, 183, 185, 187, 201, 203, 205, 209, 213, 215, 217, 219, 221, 235, 237, 247, 249, 253, 259, 265, 267, 287, 291, 295, 299, 301, 303
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OFFSET

1,1


COMMENTS

These are the odd squarefree semiprimes.
These numbers n have the property that n is a Fermat pseudoprime for at least two bases 1 < b < n  1. That is, b^(n  1) = 1 (mod n). See sequence A175101 for a count of the number of bases.  Karsten Meyer, Dec 02 2010
The new Mathematica function returns the next element of this sequence after integer n. This program is more efficient than the original one that was based on sorting and selecting.  Lei Zhou, Dec 11 2012


LINKS

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


MATHEMATICA

max = 300; A046388 = Sort@Flatten@Table[Prime[m] Prime[n], {n, 3, Ceiling[PrimePi[max/3]]}, {m, 2, n  1}]; Select[A046388, # < max &] (* Alonso del Arte based on Robert G. Wilson v's program for A006881, Oct 24 2011 *)
%t f[n_]:=Block[{p1=Prime[Range[2, PrimePi[Max[3, NextPrime[Ceiling@Sqrt[n + 1]  1]]]]], p2}, p2 = Table[Max[NextPrime[p1[[i]]], NextPrime[Ceiling[(n + 1)/p1[[i]]]  1]], {i, Length[p1]}]; Min[p1*p2]]; NestList[f, 15, 50] (* Lei Zhou, Dec 11 2012 *)


PROG

(Haskell)
a046388 n = a046388_list !! (n1)
a046388_list = filter ((== 2) . a001221) a056911_list
 Reinhard Zumkeller, Jan 02 2014
(PARI) isok(n) = (n % 2) && (bigomega(n) == 2) && (omega(n)==2); \\ Michel Marcus, Feb 05 2015


CROSSREFS

Cf. A001358, A046315, A046404.
Different from A056913, A098905, A225375.
Cf. A001221, A056911, intersection of A005117 and A046315.
Sequence in context: A225375 A146166 A024556 * A056913 A002557 A128907
Adjacent sequences: A046385 A046386 A046387 * A046389 A046390 A046391


KEYWORD

nonn


AUTHOR

Patrick De Geest, Jun 15 1998


EXTENSIONS

I removed some ambiguity in the definition and edited the entry, merging in some material from A146166.  N. J. A. Sloane, May 09 2013


STATUS

approved



