A175761 Odd nonprimes such that the arithmetic mean of all prime factors is not an integer.

1, 45, 63, 75, 99, 117, 135, 147, 153, 165, 171, 175, 207, 245, 255, 261, 273, 279, 315, 325, 333, 345, 351, 363, 369, 375, 385, 387, 399, 405, 423, 435, 455, 459, 475, 477, 495, 507, 531, 539, 549, 561, 567, 595, 603, 615, 639, 651, 657, 665, 675, 705, 711, 715, 735

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 29 2010

Keywords

• nonn
• easy

Comments

The presence of 1 (which has no prime factors) is for compatibility with A175352.

Examples

			a(6) = 117 because 117 = 3*3*13 and (3 + 3 + 13)/3 is not an integer.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A141468, A175352.

Programs

Mathematica

fQ[n_] := Block[{fi = Flatten[ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]}, len = Length@ fi; len != 1 && ! IntegerQ[ Plus @@ fi/len]]; Join[{1},Select[1 + 2 Range@ 356, fQ]] (* Robert G. Wilson v, Aug 31 2010 *)

Formula

Equals: Intersection of A175352 and A014076.

Extensions

Corrected (315, 345 inserted, 355 removed) by R. J. Mathar, Aug 30 2010