OFFSET
1,2
COMMENTS
First differs from A072774 in having 90.
First differs from A242414 in having 180.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
EXAMPLE
The prime indices of 126 are {1,2,2,4} with median 2 and distinct prime indices {1,2,4} with median 2, so 126 is in the sequence.
The prime indices of 180 are {1,1,2,2,3} with median 2 and distinct prime indices {1,2,3} with median 2, so 180 is in the sequence.
MAPLE
isA360249 := proc(n)
local ifs, pidx, pe, medAll, medDist ;
if n = 1 then
return true ;
end if ;
ifs := ifactors(n)[2] ;
pidx := [] ;
for pe in ifs do
numtheory[pi](op(1, pe)) ;
pidx := [op(pidx), seq(%, i=1..op(2, pe))] ;
end do:
medAll := stats[describe, median](sort(pidx)) ;
pidx := convert(convert(pidx, set), list) ;
medDist := stats[describe, median](sort(pidx)) ;
if medAll = medDist then
true;
else
false;
end if;
end proc:
for n from 1 to 130 do
if isA360249(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], Median[prix[#]]==Median[Union[prix[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 07 2023
STATUS
approved