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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

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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]];