A160758 Integer averages of first n nonprime numbers for some n.

1, 8, 25, 33, 359, 2948, 3291, 4959, 22350, 33357, 60907, 80962, 8276347, 11856980, 15254419, 176009996, 967538242, 1729774831, 9977169279, 193005936726

Offset: 1

Author

Daniel Tisdale, May 25 2009

Keywords

• nonn
• more

Comments

A variant of A050248 for nonprimes.

Numbers n such that (1/n)*sum(j=1..n, A018252(j)) is an integer. - Robert G. Wilson v, Jun 05 2009

Examples

			The sum of the first 44 nonprimes is 1452. 1452 / 44 = 33, hence 33 is in the sequence.
		

Crossrefs

Cf. A050248, integer averages of n primes for some n.

Cf. A018252, A051349, A164280, A129749.

Programs

Magma

S:=[]; a:=0; c:=0; for n in [1..40000000] do if not IsPrime(n) then a+:=n; c+:=1; if a mod c eq 0 then Append(~S, a div c); end if; end if; end for; S; // Klaus Brockhaus, Aug 11 2009

Mathematica

lst = {}; s = 0; c = 0; k = 1; While[k < 2700000000, If[ !PrimeQ@k, c++; s = s + k; If[Mod[s, c] == 0, AppendTo[lst, s/c]]]; k++ ]; lst (* Robert G. Wilson v, Jun 05 2009 *)
a=0;lst={};Do[If[ !PrimeQ[n],m=n;a+=m;If[a/n==IntegerPart[a/n],AppendTo[lst,a/n]]],{n,9!}];lst

Formula

a(n) = A164280(n) / A129749(n).

Extensions

a(6) - a(16) from Robert G. Wilson v, Jun 05 2009

a(17) - a(19) from Donovan Johnson, Sep 16 2009

Edited by N. J. A. Sloane, May 11 2010

a(20) from Donovan Johnson, May 20 2010