A200612 The arithmetic mean of the prime factors (with multiplicity) of n is 3.

3, 9, 20, 27, 60, 81, 112, 180, 243, 336, 400, 540, 729, 1008, 1200, 1620, 2187, 2240, 2816, 3024, 3600, 4860, 6561, 6720, 8000, 8448, 9072, 10800, 12544, 13312, 14580, 19683, 20160, 24000, 25344, 27216, 32400, 37632, 39936, 43740, 44800, 56320, 59049, 60480

Offset: 1

Author

Jeffrey Burch, Nov 19 2011

Keywords

• nonn

Examples

			20 is in the sequence because 20 = 2*2*5 and (2+2+5)/3 = 9/3 = 3.
		

Links

• Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 1..500 (first 150 terms from Reinhard Zumkeller)

Crossrefs

Subsequence of A078175.

Programs

Haskell

a200612 n = a200612_list !! (n-1)
a200612_list = filter f [2..] where
   f x = r == 0 && x' == 3 where (x',r) = divMod (a001414 x) (a001222 x)
-- Reinhard Zumkeller, Nov 20 2011

Maple

for i from 2 to 35000 do: a:=ifactors(i): s:=sum((a[2][j][1]*a[2][j][2]),j=1..nops(a[2])): t:=sum((a[2][j][2]),j=1..nops(a[2])): if s/t=3 then print(i); fi od:

Mathematica

Select[Range[61000],Mean[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[ #]]]==3&] (* Harvey P. Dale, Nov 08 2013 *)

PARI

isok(n) = my(f = factor(n)); (sum(k=1, #f~, f[k,1]*f[k,2]) / vecsum(f[,2])) == 3; \\ Michel Marcus, Feb 22 2016

Formula

A001414(a(n)) mod A001222(a(n)) = 0 and A001414(a(n))/A001222(a(n)) = 3. [Reinhard Zumkeller, Nov 20 2011]