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 A016105 Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4). 14
 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, 501, 517, 537, 553, 573, 581, 589, 597, 633, 649, 669, 681, 713, 717, 721, 737, 749, 753, 781, 789 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A084109. - Ralf Stephan and David W. Wilson, Apr 17 2005 Subsequence of A046388. - Altug Alkan, Dec 10 2015 Subsequence of A339817. No common terms with A339870. - Antti Karttunen, Dec 26 2020 Named after the Venezuelan-American computer scientist Manuel Blum (b. 1938). - Amiram Eldar, Jun 06 2021 LINKS Antti Karttunen, Table of n, a(n) for n = 1..26828; all terms < 2^19 (first 1000 terms from T. D. Noe) Joe Hurd, Blum Integers, Talk at the Trinity College, Jan 20 1997. Wikipedia, Blum integer. FORMULA a(n) = A195758(n) * A195759(n). - Reinhard Zumkeller, Sep 23 2011 MAPLE N:= 10000: # to get all terms <= N Primes:= select(isprime, [seq(i, i=3..N/3, 4)]): S:=select(`<=`, {seq(seq(Primes[i]*Primes[j], i=1..j-1), j=2..nops(Primes))}, N): sort(convert(S, list)); # Robert Israel, Dec 11 2015 MATHEMATICA With[{upto = 820}, Select[Union[Times@@@Subsets[ Select[Prime[Range[ PrimePi[ NextPrime[upto/3]]]], Mod[#, 4] == 3 &], {2}]], # <= upto &]] (* Harvey P. Dale, Aug 19 2011 *) Select[4Range[5, 197] + 1, PrimeNu[#] == 2 && MoebiusMu[#] == 1 && Mod[FactorInteger[#][[1, 1]], 4] != 1 &] (* Alonso del Arte, Nov 18 2015 *) PROG (Haskell) import Data.Set (singleton, fromList, deleteFindMin, union) a016105 n = a016105_list !! (n-1) a016105_list = f [3, 7] (drop 2 a002145_list) 21 (singleton 21) where    f qs (p:p':ps) t s      | m < t     = m : f qs (p:p':ps) t s'      | otherwise = m : f (p:qs) (p':ps) t' (s' `union` (fromList pqs))      where (m, s') = deleteFindMin s            t' = head \$ dropWhile (> 3*p') pqs            pqs = map (p *) qs -- Reinhard Zumkeller, Sep 23 2011 (Perl) use ntheory ":all"; forcomposites { say if (\$_ % 4) == 1 && is_square_free(\$_) && scalar(factor(\$_)) == 2 && !scalar(grep { (\$_ % 4) != 3 } factor(\$_)); } 10000; # Dana Jacobsen, Dec 10 2015 (PARI) list(lim)=my(P=List(), v=List(), t, p); forprime(p=2, lim\3, if(p%4==3, listput(P, p))); for(i=2, #P, p=P[i]; for(j=1, i-1, t=p*P[j]; if(t>lim, break); listput(v, t))); Set(v) \\ Charles R Greathouse IV, Jul 01 2016 (PARI) isA016105(n) = (2==omega(n)&&2==bigomega(n)&&1==(n%4)&&3==((factor(n)[1, 1])%4)); \\ Antti Karttunen, Dec 26 2020 (Python) from sympy import factorint def ok(n):     fn = factorint(n)     return len(fn) == sum(fn.values()) == 2 and all(f%4 == 3 for f in fn) print([k for k in range(790) if ok(k)]) # Michael S. Branicky, Dec 20 2021 CROSSREFS Cf. A002145, A006881, A046388, A339870. Intersection of A005117 and A107978. Also, subsequence of the following sequences: A046388, A084109, A091113, A167181, A339817. Sequence in context: A190299 A280262 A084109 * A187073 A271101 A191683 Adjacent sequences:  A016102 A016103 A016104 * A016106 A016107 A016108 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Erich Friedman STATUS approved

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Last modified July 1 10:54 EDT 2022. Contains 354972 sequences. (Running on oeis4.)