A033286 a(n) = n * prime(n).

2, 6, 15, 28, 55, 78, 119, 152, 207, 290, 341, 444, 533, 602, 705, 848, 1003, 1098, 1273, 1420, 1533, 1738, 1909, 2136, 2425, 2626, 2781, 2996, 3161, 3390, 3937, 4192, 4521, 4726, 5215, 5436, 5809, 6194, 6513, 6920, 7339, 7602, 8213, 8492, 8865, 9154, 9917

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Sums of rows of the triangle in A005145. - Reinhard Zumkeller, Aug 05 2009

Complement of A171520(n). - Jaroslav Krizek, Dec 13 2009

Partial sums of A090942. - Omar E. Pol, Apr 20 2015

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Albert Frank, International Contest Of Logical Sequences, 2002 - 2003. Item 1.
• Albert Frank, Solutions of International Contest Of Logical Sequences, 2002 - 2003.

Crossrefs

Cf. A000040, A007504, A014689, A090942, A124012, A141042, A152535.

Cf. A005145 (primes repeated), A171520 (complement), A076146 (iterated).

Programs

Haskell

a033286 n = a000040 n * n  -- Reinhard Zumkeller, Jul 24 2013

Magma

[ n*NthPrime(n): n in [1..47] ]; // Klaus Brockhaus, Sep 09 2009

Maple

A033286 := proc(n) n*ithprime(n) ; end proc:
seq(A033286(n),n=1..20) ; # R. J. Mathar, Mar 21 2011

Mathematica

Table[Prime[n]*n, {n, 38}] (* Alonso del Arte *)

MuPAD

ithprime(i)*i $ i = 1..47 // Zerinvary Lajos, Feb 26 2007

PARI

a(n)=n*prime(n) \\ Charles R Greathouse IV, Jul 01 2013

Formula

a(n) = n * A000040(n) = n * A008578(n+1) = n * A158611(n+2). - Jaroslav Krizek, Aug 31 2009

a(n) = A007504(n) + A152535(n). - Omar E. Pol, Aug 09 2012

Sum_{n>=1} 1/a(n) = A124012. - Amiram Eldar, Oct 15 2020

Extensions

Correction for change of offset in A158611 and A008578 in Aug 2009 from Jaroslav Krizek, Jan 27 2010