A174894 Numbers such that the arithmetic mean of their distinct prime factors and the arithmetic mean of all of their prime factors are both integers.

2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 42, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 77, 78, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 101

Offset

1,1

Comments

Subsequence of A078174 and A078175.

Complement of A176552. [From Jaroslav Krizek, Apr 21 2010]

Links

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

Example

For a(11) = 16: 16 = 2^4; both (2+2+2+2)/4 and 2/1 are integers.

Mathematica

mdmaQ[n_]:=With[{fi=FactorInteger[n]}, AllTrue[{Mean[Flatten[Table[#[[1]], #[[2]]]&/@fi]], Mean[fi[[;; , 1]]]}, IntegerQ]]; Select[Range[ 2, 110], mdmaQ] (* Harvey P. Dale, Nov 16 2024 *)

Crossrefs

Sequence in context: A360552 A373852 A078174 * A275616 A088948 A369096

Adjacent sequences: A174891 A174892 A174893 * A174895 A174896 A174897

Keyword

nonn

Author

Jaroslav Krizek, Apr 01 2010

Extensions

Definition clarified by Harvey P. Dale, Nov 16 2024

Status

approved