login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A016105 Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4). 8
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

LINKS

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

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

CROSSREFS

Cf. A002145, A006881, A046388.

Sequence in context: A190299 A280262 A084109 * A187073 A271101 A191683

Adjacent sequences:  A016102 A016103 A016104 * A016106 A016107 A016108

KEYWORD

nonn,easy,nice

AUTHOR

Robert G. Wilson v

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 08:40 EST 2018. Contains 317347 sequences. (Running on oeis4.)