This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033286 #58 Sep 08 2022 08:44:51
%S A033286 2,6,15,28,55,78,119,152,207,290,341,444,533,602,705,848,1003,1098,
%T A033286 1273,1420,1533,1738,1909,2136,2425,2626,2781,2996,3161,3390,3937,
%U A033286 4192,4521,4726,5215,5436,5809,6194,6513,6920,7339,7602,8213,8492,8865,9154,9917
%N A033286 a(n) = n * prime(n).
%C A033286 Does an n exist such that n*prime(n)/(n+prime(n)) is an integer? - _Ctibor O. Zizka_, Mar 04 2008. The answer to Zizka's question is easily seen to be No: such an integer k would be positive and less than prime(n), but then k*(n + prime(n)) = prime(n)*n would be impossible. - _Robert Israel_, Apr 20 2015
%C A033286 Sums of rows of the triangle in A005145. - _Reinhard Zumkeller_, Aug 05 2009
%C A033286 Complement of A171520(n). - _Jaroslav Krizek_, Dec 13 2009
%C A033286 Partial sums of A090942. - _Omar E. Pol_, Apr 20 2015
%H A033286 Reinhard Zumkeller, <a href="/A033286/b033286.txt">Table of n, a(n) for n = 1..10000</a>
%H A033286 Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003.html">International Contest Of Logical Sequences</a>, 2002 - 2003. Item 1.
%H A033286 Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003ans.html">Solutions of International Contest Of Logical Sequences</a>, 2002 - 2003.
%F A033286 a(n) = n * A000040(n) = n * A008578(n+1) = n * A158611(n+2). - _Jaroslav Krizek_, Aug 31 2009
%F A033286 a(n) = A007504(n) + A152535(n). - _Omar E. Pol_, Aug 09 2012
%F A033286 Sum_{n>=1} 1/a(n) = A124012. - _Amiram Eldar_, Oct 15 2020
%p A033286 A033286 := proc(n) n*ithprime(n) ; end proc:
%p A033286 seq(A033286(n),n=1..20) ; # _R. J. Mathar_, Mar 21 2011
%t A033286 Table[Prime[n]*n, {n, 38}] (* _Alonso del Arte_ *)
%o A033286 (MuPAD) ithprime(i)*i $ i = 1..47 // _Zerinvary Lajos_, Feb 26 2007
%o A033286 (Magma) [ n*NthPrime(n): n in [1..47] ]; // _Klaus Brockhaus_, Sep 09 2009
%o A033286 (PARI) a(n)=n*prime(n) \\ _Charles R Greathouse IV_, Jul 01 2013
%o A033286 (Haskell)
%o A033286 a033286 n = a000040 n * n -- _Reinhard Zumkeller_, Jul 24 2013
%Y A033286 Cf. A000040, A007504, A014689, A090942, A124012, A141042, A152535.
%Y A033286 Cf. A005145 (primes repeated), A171520 (complement), A076146 (iterated).
%K A033286 nonn,easy
%O A033286 1,1
%A A033286 _N. J. A. Sloane_
%E A033286 Correction for change of offset in A158611 and A008578 in Aug 2009 from _Jaroslav Krizek_, Jan 27 2010