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Odious numbers (A000069) that are the product of exactly two distinct primes.
3

%I #18 May 21 2024 16:41:44

%S 14,21,22,26,35,38,55,62,69,74,82,87,91,93,94,115,118,122,133,134,143,

%T 145,146,155,158,161,185,194,203,205,206,213,214,217,218,247,253,254,

%U 259,262,265,274,295,299,301,302,309,314,319,321,327,334,339,341,346

%N Odious numbers (A000069) that are the product of exactly two distinct primes.

%H Charles R Greathouse IV, <a href="/A230095/b230095.txt">Table of n, a(n) for n = 1..10000</a>

%H E. Fouvry, C. Mauduit, <a href="http://dx.doi.org/10.1007/BF01444238">Sommes des chiffres et nombres presque premiers</a>, (French) [Sums of digits and almost primes] Math. Ann. 305 (1996), no. 3, 571--599. MR1397437 (97k:11029).

%t Select[Range[400],OddQ[DigitCount[#,2,1]]&&PrimeNu[#]==PrimeOmega[#]==2&] (* _Harvey P. Dale_, May 21 2024 *)

%o (PARI) isodious(n)=b = binary(n); sum(i=1, #b, b[i]==1) % 2;

%o isok(n) = isodious(n) && (bigomega(n)==2) && (omega(n)==2); \\ _Michel Marcus_, Oct 12 2013

%o (PARI) list(lim)=my(v=List()); forprime(p=2,lim\2, forprime(q=2,min(lim\p,p-1), if(hammingweight(p*q)%2, listput(v,p*q)))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017

%Y Cf. A000069, A027697, A130593.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Oct 11 2013

%E More terms from _Michel Marcus_, Oct 12 2013