A134335 Numbers such that the arithmetic mean of their prime factors (counted with multiplicity) is an integer, but not a prime.

15, 35, 39, 42, 50, 51, 55, 65, 77, 78, 87, 91, 92, 95, 110, 111, 114, 115, 119, 123, 140, 141, 143, 155, 159, 161, 164, 170, 183, 185, 186, 187, 189, 201, 203, 204, 209, 215, 219, 221, 222, 225, 230, 235, 236, 242, 247, 258, 259, 264, 267, 284, 285, 287, 290

Offset: 1

Author

Hieronymus Fischer, Oct 23 2007

Keywords

• nonn

Examples

			a(1) = 15, since 15 = 3*5 and (3+5)/2 = 4 is not prime.
a(5) = 50, since 50 = 2*5*5 and (2+5+5)/3 = 4 is not prime.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001222, A100118, A046363, A133620, A133621.

Cf. A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134334.

Programs

Mathematica

fp[{a_,b_}]:=a*b;s={};Do[If[q=Total[fp/@FactorInteger[n]]/Total[Last/@FactorInteger[n]];IntegerQ[q]&&!PrimeQ[q],AppendTo[s,n]],{n,2,290}];s (* James C. McMahon, Apr 05 2025 *)

Extensions

Definition clarified by the author, May 06 2013