A070005 Arithmetic mean of prime factors of n is an integer and n is neither a prime nor power of a prime.

15, 21, 33, 35, 39, 42, 45, 51, 55, 57, 63, 65, 69, 75, 77, 78, 84, 85, 87, 91, 93, 95, 99, 105, 110, 111, 114, 115, 117, 119, 123, 126, 129, 133, 135, 141, 143, 145, 147, 153, 155, 156, 159, 161, 168, 170, 171, 175, 177, 183, 185, 186, 187, 189, 195, 201, 203

Offset: 1

Author

Labos Elemer, Apr 11 2002

Keywords

• easy
• nonn

Examples

			n=33=3*11, mean=(3+11)/2=6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070006, A001414, A008472.

Cf. A000961, A010055; subsequence of A078174.

Programs

Haskell

a070005 n = a070005_list !! (n-1)
a070005_list = filter ((== 0) . a010055) a078174_list
-- Reinhard Zumkeller, Jun 01 2013

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] Do[s=Apply[Plus, ba[n]]/lf[n]; If[IntegerQ[s]&&Greater[lf[n], 1], Print[n]], {n, 2, 1000}]

PARI

lista(nn) = {for (n=2, nn, f = factor(n); if ((#f~ != 1) && (sum(k=1, #f~, f[k,1]) % #f~ == 0), print1(n, ", ")););} \\ Michel Marcus, Mar 28 2015