OFFSET
1,1
COMMENTS
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 84 are {1,1,2,4}, with maximum 4 and median 3/2, and 4 > 2*(3/2), so 84 is in the sequence.
The terms together with their prime indices begin:
20: {1,1,3}
28: {1,1,4}
40: {1,1,1,3}
44: {1,1,5}
52: {1,1,6}
56: {1,1,1,4}
66: {1,2,5}
68: {1,1,7}
76: {1,1,8}
78: {1,2,6}
80: {1,1,1,1,3}
84: {1,1,2,4}
88: {1,1,1,5}
92: {1,1,9}
99: {2,2,5}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Max@@prix[#]>2*Median[prix[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2023
STATUS
approved