OFFSET
1,2
COMMENTS
EXAMPLE
The terms together with their prime indices begin:
1: {}
2: {1}
9: {2,2}
88: {1,1,1,5}
100: {1,1,3,3}
125: {3,3,3}
624: {1,1,1,1,2,6}
756: {1,1,2,2,2,4}
792: {1,1,1,2,2,5}
810: {1,2,2,2,2,3}
880: {1,1,1,1,3,5}
900: {1,1,2,2,3,3}
1312: {1,1,1,1,1,13}
2401: {4,4,4,4}
4617: {2,2,2,2,2,8}
4624: {1,1,1,1,7,7}
6240: {1,1,1,1,1,2,3,6}
7392: {1,1,1,1,1,2,4,5}
7560: {1,1,1,2,2,2,3,4}
7920: {1,1,1,1,2,2,3,5}
Example: 810 has prime indices {1,2,2,2,2,3} and prime exponents (1,4,1), both of which have mean 2, so 810 is in the sequence.
Example: 78720 has prime indices {1,1,1,1,1,1,1,2,3,13} and prime exponents (7,1,1,1), both of which have mean 5/2, so 78720 is in the sequence.
MATHEMATICA
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
prisig[n_]:=If[n==1, {}, Last/@FactorInteger[n]];
Select[Range[1000], Mean[prix[#]]==Mean[prisig[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 24 2023
STATUS
approved