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A078175
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Numbers with an integer arithmetic mean of all prime factors.
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47
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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2100=2*2*3*5*5*7: (2+2+3+5+5+7)/6=4, therefore 2100 is a term.
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MATHEMATICA
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sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
filterQ[n_] := Divisible[sopfr[n], PrimeOmega[n]];
iamQ[n_]:=IntegerQ[Mean[Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[ n]]]]; Select[Range[2, 150], iamQ] (* Harvey P. Dale, Jun 23 2021 *)
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PROG
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(Haskell)
a078175 n = a078175_list !! (n-1)
a078175_list = filter (\x -> (a001414 x) `mod` (a001222 x) == 0) [2..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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