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 A100484 Even semiprimes. 113

%I

%S 4,6,10,14,22,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,

%T 158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,

%U 334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514,526

%N Even semiprimes.

%C Essentially the same as A001747.

%C Twice the prime numbers. - _Omar E. Pol_, May 14 2008

%C Right edge of the triangle in A065342. - _Reinhard Zumkeller_, Jan 30 2012

%C Solutions of the differential equation n' = 1/2*(n+4), where n' is the arithmetic derivative of n. - _Paolo P. Lava_, Feb 02 2012

%C A253046(a(n)) > a(n). - _Reinhard Zumkeller_, Dec 26 2014

%C Apart from the first term, numbers k such that k = sigma(k) - phi(k) - d(k). - _Paolo P. Lava_, Mar 01 2017

%C Apart from first term, these are the tau2-primes as defined in [Anderson, Frazier] and [Lanterman]. - _Michel Marcus_, May 15 2019

%H Charles R Greathouse IV, <a href="/A100484/b100484.txt">Table of n, a(n) for n = 1..10000</a>

%H D. D. Anderson and Andrea M. Frazier, <a href="https://doi.org/10.1216/RMJ-2011-41-3-663">On a general theory of factorization in integral domains</a>, Rocky Mountain J. Math., Volume 41, Number 3 (2011), 663-705. See pp. 698, 699, 702.

%H James Lanterman, <a href="https://arxiv.org/abs/1210.2991">Irreducibles in the Integers modulo n</a>, arXiv:1210.2991 [math.NT], 2012.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>

%F a(n) = 2 * A000040(n).

%F a(n) = A001747(n+1).

%F n>1: A000005(a(n)) = 4; A000203(a(n)) = 3*A008864(n); A000010(a(n)) = A006093(n); intersection of A001358 and A005843.

%F a(n) = A116366(n-1, n-1) for n>1. - _Reinhard Zumkeller_, Feb 06 2006

%F a(n) = A077017(n+1), n>1. - _R. J. Mathar_, Sep 02 2008

%F A078834(a(n)) = A000040(n). - _Reinhard Zumkeller_, Sep 19 2011

%F a(n) = A087112(n, 1). - _Reinhard Zumkeller_, Nov 25 2012

%F A000203(a(n)) = 3*n/2 + 3, n > 1. - _Wesley Ivan Hurt_, Sep 07 2013

%p A100484:=n->2*ithprime(n); seq(A100484(n), n=1..70); # _Wesley Ivan Hurt_, Mar 27 2014

%t 2*Prime[Range] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)

%o (PARI) 2*primes(70) \\ _Charles R Greathouse IV_, Aug 21 2011

%o a100484 n = a100484_list !! (n-1)

%o a100484_list = map (* 2) a000040_list

%o -- _Reinhard Zumkeller_, Jan 31 2012

%o (MAGMA) [2*p: p in PrimesUpTo(350)]; // _Vincenzo Librandi_, Mar 27 2014

%o (GAP) 2*Filtered([1..300],IsPrime); # _Muniru A Asiru_, Oct 05 2018

%o (GAP) List([1..70], n-> 2*Primes[n]) # _G. C. Greubel_, May 18 2019

%o (Sage) [2*nth_prime(n) for n in (1..70)] # _G. C. Greubel_, May 18 2019

%Y Subsequence of A091376.

%Y Cf. A046315, A152099, A179740.

%Y Cf. A001748, A253046.

%Y Row 3 of A286625, column 3 of A286623.

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Nov 22 2004

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Last modified July 6 00:43 EDT 2020. Contains 335475 sequences. (Running on oeis4.)