OFFSET
1,2
COMMENTS
EXAMPLE
The prime indices of 900 are {3,3,2,2,1,1} with mean 2, and the distinct prime indices are {1,2,3} also with mean 2, so 900 is in the sequence.
MAPLE
isA360247 := proc(n)
local ifs, pidx, pe, meanAll, meanDist ;
if n = 1 then
return true ;
end if ;
ifs := ifactors(n)[2] ;
# list of prime indices with multiplicity
pidx := [] ;
for pe in ifs do
[numtheory[pi](op(1, pe)), op(2, pe)] ;
pidx := [op(pidx), %] ;
end do:
meanAll := add(op(1, pe)*op(2, pe), pe=pidx) / add(op(2, pe), pe=pidx) ;
meanDist := add(op(1, pe), pe=pidx) / nops(pidx) ;
if meanAll = meanDist then
true;
else
false;
end if;
end proc:
for n from 1 to 130 do
if isA360247(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, May 22 2023
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Mean[prix[#]]==Mean[Union[prix[#]]]&]
CROSSREFS
These partitions are counted by A360243.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 07 2023
STATUS
approved