Search: id:A046388
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%I A046388
%S A046388 15,21,33,35,39,45,51,55,57,63,65,69,75,77,85,87,91,93,95,99,111,115,
%T A046388 117,119,123,129,133,135,141,143,145,147,153,155,159,161,171,175,177,
%U A046388 183,185,187,189,201,203,205,207,209,213,215,217,219,221,225,235,237
%N A046388 Odd numbers with exactly 2 distinct prime factors.
%C A046388 Comments from Karsten Meyer (arbol01(AT)gmx.de), Oct 07 2007: (Start) 
               Each term n=a*b of the sequence is at least a Fermat pseudoprime 
               to the two bases a1 and a2 which have the property that |p*a - q*b| 
               = 2 and a is the number between p*a and q*b. There are no more bases 
               of this form below of the number n.
%C A046388 There may be exists other bases below the number n, but just two bases 
               have the property that they a direct neigbours of a multiple of a 
               and a multiple of b. For example, 39=3*13 is a Fermat pseudoprime 
               to the bases 14 and 25 because 14 is the number between 13 and 3*5 
               and 25 is the number between 3*8 and 2*13.
%C A046388 91=7*13 is a Fermat pseudoprime to the bases 27 and 64 because 27 is 
               the number between 2*13 and 4*7 and 64 is the number between 9*7 
               and 5*13. For 91 exists although the bases 3, 4, 9, 10, 12, 16, 17, 
               22, 23, 25, 29, 30, 36, 38, 40, 43, 48, 51, 53, 55, 61, 62, 66, 68, 
               69, 74, 75, 79, 81, 82, 87, 88. But neither of them lies between 
               a multiple of 7 and a multiple of 13. (End)
%C A046388 Subset of A098905 (which contains in addition A046390 and numbers like 
               255255, 285285, 345345, 373065 etc). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 13 2008]
%p A046388 A001221 := proc(n) nops(numtheory[factorset](n)) ; end: isA046388 := 
               proc(n) RETURN( (n mod 2 = 1) and (A001221(n) = 2) ); end: for n 
               from 1 to 840 do if isA046388(n) then printf("%d,",n) ; fi; od: [From 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 13 2008]
%Y A046388 Cf. A046315, A046404, A024556, A056913.
%Y A046388 Sequence in context: A070537 A070005 A061346 this_sequence A098905 A024556 
               A146166
%Y A046388 Adjacent sequences: A046385 A046386 A046387 this_sequence A046389 A046390 
               A046391
%K A046388 nonn
%O A046388 1,1
%A A046388 Patrick De Geest (pdg(AT)worldofnumbers.com), Jun 15 1998.
%E A046388 Inserted 45, 63, 75, 99, 117, 135 etc. by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 13 2008

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