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

1,1

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.

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

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 *)

Prog

(MuPAD) ithprime(i)*i $ i = 1..47 // Zerinvary Lajos, Feb 26 2007
(Magma) [ n*NthPrime(n): n in [1..47] ]; // Klaus Brockhaus, Sep 09 2009
(PARI) a(n)=n*prime(n) \\ Charles R Greathouse IV, Jul 01 2013
(Haskell)
a033286 n = a000040 n * n  -- Reinhard Zumkeller, Jul 24 2013

Crossrefs

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

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

Sequence in context: A138621 A163061 A331773 * A182724 A374218 A342163

Adjacent sequences: A033283 A033284 A033285 * A033287 A033288 A033289

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved