A160758 - OEIS

%I #12 Sep 08 2022 08:45:45

%S 1,8,25,33,359,2948,3291,4959,22350,33357,60907,80962,8276347,

%T 11856980,15254419,176009996,967538242,1729774831,9977169279,

%U 193005936726

%N Integer averages of first n nonprime numbers for some n.

%C A variant of A050248 for nonprimes.

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

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

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

%t 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 *)

%t a=0;lst={};Do[If[ !PrimeQ[n],m=n;a+=m;If[a/n==IntegerPart[a/n],AppendTo[lst,a/n]]],{n,9!}];lst

%o (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

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

%Y Cf. A018252, A051349, A164280, A129749.

%K nonn,more

%O 1,2

%A _Daniel Tisdale_, May 25 2009

%E a(6) - a(16) from _Robert G. Wilson v_, Jun 05 2009

%E a(17) - a(19) from _Donovan Johnson_, Sep 16 2009

%E Edited by _N. J. A. Sloane_, May 11 2010

%E a(20) from _Donovan Johnson_, May 20 2010