A175758 Numbers n with property that arithmetic mean of its digits is both an integer and one of the prime factors of n.

2, 3, 5, 7, 15, 22, 24, 33, 40, 42, 51, 55, 60, 77, 108, 114, 117, 126, 132, 135, 144, 150, 153, 162, 171, 180, 195, 204, 207, 216, 222, 225, 234, 240, 243, 252, 261, 270, 285, 306, 312, 315, 324, 330, 333, 342, 351, 360, 375, 399, 402, 405, 414, 420, 423, 432

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 28 2010, Aug 29 2010

Keywords

• nonn
• base

Examples

			15 is in the list because (1+5)/2=3 and 3 is a prime factor of 15.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A027746, A175688.

Programs

Mathematica

ipfQ[n_]:=Module[{m=Mean[IntegerDigits[n]]},IntegerQ[m]&&MemberQ[ FactorInteger[ n][[All,1]],m]]; Select[Range[2,500],ipfQ] (* Harvey P. Dale, Feb 15 2020 *)

Extensions

399 inserted by D. S. McNeil, Sep 27 2010