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.
FORMULA
Disjoint from A361909.
EXAMPLE
The terms together with their prime indices begin:
4: {1,1}
24: {1,1,1,2}
36: {1,1,2,2}
54: {1,2,2,2}
81: {2,2,2,2}
160: {1,1,1,1,1,3}
240: {1,1,1,1,2,3}
360: {1,1,1,2,2,3}
400: {1,1,1,1,3,3}
540: {1,1,2,2,2,3}
600: {1,1,1,2,3,3}
810: {1,2,2,2,2,3}
896: {1,1,1,1,1,1,1,4}
900: {1,1,2,2,3,3}
1000: {1,1,1,3,3,3}
1215: {2,2,2,2,2,3}
1344: {1,1,1,1,1,1,2,4}
1350: {1,2,2,2,3,3}
1500: {1,1,2,3,3,3}
2016: {1,1,1,1,1,2,2,4}
2025: {2,2,2,2,3,3}
2240: {1,1,1,1,1,1,3,4}
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Length[prix[#]]==2*Max[prix[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2023
STATUS
approved