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.

24, 36, 40, 54, 56, 88, 96, 100, 104, 135, 136, 144, 152, 160, 184, 189, 196, 216, 224, 225, 232, 240, 248, 250, 296, 297, 324, 328, 336, 344, 351, 352, 360, 375, 376, 384, 400, 416, 424, 441, 459, 472, 484, 486, 488, 504, 513, 528, 536, 540, 544, 560, 568

Offset: 1

Author

Labos Elemer, Jan 16 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A001222, A067340.

Programs

Mathematica

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}]

PARI

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

Formula

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