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
Keywords
Examples
For a(11) = 16: 16 = 2^4; both (2+2+2+2)/4 and 2/1 are integers.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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 *)
Extensions
Definition clarified by Harvey P. Dale, Nov 16 2024
Comments