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 A046388 Odd numbers of the form p*q where p and q are distinct primes. 76

%I

%S 15,21,33,35,39,51,55,57,65,69,77,85,87,91,93,95,111,115,119,123,129,

%T 133,141,143,145,155,159,161,177,183,185,187,201,203,205,209,213,215,

%U 217,219,221,235,237,247,249,253,259,265,267,287,291,295,299,301,303

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

%C These are the odd squarefree semiprimes.

%C 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

%H Amiram Eldar, <a href="/A046388/b046388.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)

%F Sum_{n>=1} 1/a(n)^s = (1/2)*(P(s)^2 - P(2*s)) + 1/4^s - P(s)/2^s, for s>1, where P is the prime zeta function. - _Amiram Eldar_, Nov 21 2020

%t 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 *)

%o a046388 n = a046388_list !! (n-1)

%o a046388_list = filter ((== 2) . a001221) a056911_list

%o -- _Reinhard Zumkeller_, Jan 02 2014

%o (PARI) isok(n) = (n % 2) && (bigomega(n) == 2) && (omega(n)==2); \\ _Michel Marcus_, Feb 05 2015

%Y Intersection of A005117 and A046315.

%Y Subsequence of A024556. - _Zak Seidov_, May 28 2020

%Y Cf. A001358, A046404.

%Y Different from A056913, A098905, A225375.

%Y Cf. A001221, A056911.

%K nonn

%O 1,1

%A _Patrick De Geest_, Jun 15 1998

%E I removed some ambiguity in the definition and edited the entry, merging in some material from A146166. - _N. J. A. Sloane_, May 09 2013

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)