A134617 Numbers such that the arithmetic mean of the squares of their prime factors (taken with multiplicity) is a prime.

15, 20, 21, 28, 35, 39, 44, 48, 51, 52, 55, 65, 69, 85, 91, 92, 95, 108, 112, 115, 116, 129, 135, 141, 145, 159, 164, 172, 188, 189, 205, 208, 209, 215, 221, 225, 235, 236, 245, 249, 259, 268, 272, 295, 297, 299, 305, 309, 315, 316, 320, 325, 329, 339, 341, 365

Offset: 1

Author

Hieronymus Fischer, Nov 11 2007

Keywords

• nonn

Examples

			a(2)=20, since 20=2*2*5 and (2^2+2^2+5^2)/3=33/3=11.
		

Links

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

Crossrefs

Cf. A001597, A025475, A134333, A134344, A134376.

Cf. A134600, A134602, A134605, A134608, A134613, A134619, A134621.

Programs

Mathematica

amspQ[n_]:=PrimeQ[Mean[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[ n]]^2]]; Select[Range[400],amspQ] (* Harvey P. Dale, Jan 21 2017 *)

Extensions

Minor edits by the author, May 06 2013