OFFSET
1,1
LINKS
Wikipedia, Geometric mean
EXAMPLE
36 has two such factorizations: (3*12) and (4*9).
The sequence of terms together with their prime indices begins:
36: {1,1,2,2}
64: {1,1,1,1,1,1}
100: {1,1,3,3}
144: {1,1,1,1,2,2}
196: {1,1,4,4}
216: {1,1,1,2,2,2}
256: {1,1,1,1,1,1,1,1}
324: {1,1,2,2,2,2}
400: {1,1,1,1,3,3}
484: {1,1,5,5}
512: {1,1,1,1,1,1,1,1,1}
576: {1,1,1,1,1,1,2,2}
676: {1,1,6,6}
784: {1,1,1,1,4,4}
900: {1,1,2,2,3,3}
1000: {1,1,1,3,3,3}
1024: {1,1,1,1,1,1,1,1,1,1}
1156: {1,1,7,7}
1296: {1,1,1,1,2,2,2,2}
1444: {1,1,8,8}
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Select[Range[1000], Length[Select[facs[#], !IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]]>1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved