OFFSET
1,1
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
All terms are odd because any even number is divisible by 2 and 2's prime index is 1 which is not composite. - Harvey P. Dale, Jul 29 2026
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
The sequence of terms begins:
49 = prime(4)^2
91 = prime(4)*prime(6)
133 = prime(4)*prime(8)
161 = prime(4)*prime(9)
169 = prime(6)^2
203 = prime(4)*prime(10)
247 = prime(6)*prime(8)
259 = prime(4)*prime(12)
299 = prime(6)*prime(9)
301 = prime(4)*prime(14)
329 = prime(4)*prime(15)
343 = prime(4)^3
361 = prime(8)^2
371 = prime(4)*prime(16)
377 = prime(6)*prime(10)
427 = prime(4)*prime(18)
437 = prime(8)*prime(9)
481 = prime(6)*prime(12)
497 = prime(4)*prime(20)
511 = prime(4)*prime(21)
529 = prime(9)^2
551 = prime(8)*prime(10)
553 = prime(4)*prime(22)
559 = prime(6)*prime(14)
611 = prime(6)*prime(15)
623 = prime(4)*prime(24)
637 = prime(4)^2*prime(6)
MATHEMATICA
Select[Range[2, 1000], And[OddQ[#], !PrimeQ[#], And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]]&]
(* Alternative: *)
Select[Range[3, 1100, 2], CompositeQ[#]&&AllTrue[PrimePi[FactorInteger[#][[;; , 1]]], CompositeQ]&] (* Harvey P. Dale, Jul 29 2026 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 18 2018
STATUS
approved