A053767 Sum of first n composite numbers.

0, 4, 10, 18, 27, 37, 49, 63, 78, 94, 112, 132, 153, 175, 199, 224, 250, 277, 305, 335, 367, 400, 434, 469, 505, 543, 582, 622, 664, 708, 753, 799, 847, 896, 946, 997, 1049, 1103, 1158, 1214, 1271, 1329, 1389, 1451, 1514, 1578, 1643, 1709, 1777, 1846, 1916, 1988

Offset: 0

Author

G. L. Honaker, Jr., Mar 29 2000

Keywords

• nonn

Comments

a(A196415(n)) = A036691(A196415(n)) / A141092(n). - Reinhard Zumkeller, Oct 03 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• C. Rivera, See also

Crossrefs

Cf. A002808, A051349.

First differences of A023539.

Programs

Haskell

a053767 n = a053767_list !! (n-1)
a053767_list = scanl1 (+) a002808_list -- Reinhard Zumkeller, Oct 03 2011

Maple

A053767 := proc(n)
        add(A002808(i),i=1..n) ;
end proc: # R. J. Mathar, Oct 03 2011
ListTools[PartialSums](remove(isprime,[$2..1000])); # Robert Israel, Jan 09 2015

Mathematica

lst={};s=0;Do[If[ !PrimeQ[n], s=s+n;AppendTo[lst, s]], {n, 2, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)
Accumulate[Complement[Range[2,100],Prime[Range[PrimePi[100]]]]] (* Harvey P. Dale, Dec 28 2010 *)
Accumulate[Select[Range[2, 100], ! PrimeQ[#] &]]

PARI

lista(nn) = {my(s=0); forcomposite(n=0, nn, print1(s, ", "); s += n;);} \\ Michel Marcus, Jan 09 2015

Formula

a(n) = A000217(A002808(n)) - A034387(A002808(n)) - 1 . - Robert Israel, Jan 09 2015

a(n) = A051349(n+1) - 1. - Michel Marcus, Feb 16 2018

Extensions

a(0)=0 prepended by Max Alekseyev, Feb 10 2018