A078175 Numbers with an integer arithmetic mean of all prime factors.

2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 20, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 42, 43, 44, 47, 49, 50, 51, 53, 55, 57, 59, 60, 61, 64, 65, 67, 68, 69, 71, 73, 77, 78, 79, 81, 83, 85, 87, 89, 91, 92, 93, 95, 97, 101, 103, 105, 107, 109, 110, 111, 112, 113

Offset

1,1

Comments

A001414(a(n)) == 0 modulo A001222(a(n)).

Links

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

Example

2100=2*2*3*5*5*7: (2+2+3+5+5+7)/6=4, therefore 2100 is a term.

Mathematica

sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
filterQ[n_] := Divisible[sopfr[n], PrimeOmega[n]];
Select[Range[2, 1000], filterQ] (* Jean-François Alcover, Apr 06 2021 *)
iamQ[n_]:=IntegerQ[Mean[Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[ n]]]]; Select[Range[2, 150], iamQ] (* Harvey P. Dale, Jun 23 2021 *)

Prog

(Haskell)
a078175 n = a078175_list !! (n-1)
a078175_list = filter (\x -> (a001414 x) `mod` (a001222 x) == 0) [2..]
-- Reinhard Zumkeller, Nov 20 2011

Crossrefs

Cf. A001222, A001414, A078174.

Subsequences: A000040, A000079, A200612.

Sequence in context: A293205 A046687 A175418 * A213715 A360552 A373852

Adjacent sequences: A078172 A078173 A078174 * A078176 A078177 A078178

Keyword

nonn

Author

Reinhard Zumkeller, Nov 20 2002

Status

approved