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A067341 Number of prime factors divided by the number of distinct prime factors is an integer and n is neither squarefree, nor power of prime. 1

%I #12 Oct 21 2019 11:23:36

%S 24,36,40,54,56,88,96,100,104,135,136,144,152,160,184,189,196,216,224,

%T 225,232,240,248,250,296,297,324,328,336,344,351,352,360,375,376,384,

%U 400,416,424,441,459,472,484,486,488,504,513,528,536,540,544,560,568

%N Number of prime factors divided by the number of distinct prime factors is an integer and n is neither squarefree, nor power of prime.

%H Amiram Eldar, <a href="/A067341/b067341.txt">Table of n, a(n) for n = 1..10000</a>

%F A001222(n)/A001221(n) is integer, A001222(n)>A001221(n)>1.

%t ff[x_] := Flatten[FactorInteger[x]] f1[x_] := Length[FactorInteger[x]] f2[x_] := Apply[Plus, Table[Part[ff[x], 2*w], {w, 1, f1[x]}]] Do[s=f2[n]/f1[n]; If[IntegerQ[s]&&Greater[s, 1]&&Greater[f1[n], 1], Print[n]], {n, 2, 10000}]

%o (PARI) is(n)=my(f=factor(n)[, 2]); #f>1 && vecsum(f)%#f==0 && vecmax(f)>1 \\ _Charles R Greathouse IV_, Oct 15 2015

%Y Cf. A001221, A001222, A067340.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 16 2002

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