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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = (Product_{p prime-indexed prime} (1 + Sum_{q prime} 1/p^q)) - (Sum_{p prime-indexed prime} Sum_{q prime} 1/p^q) - 1 = 0.0106862606... . - Amiram Eldar, Aug 04 2024
EXAMPLE
The terms together with their prime indices (not factors) begin:
225: {2,2,3,3}
675: {2,2,2,3,3}
1089: {2,2,5,5}
1125: {2,2,3,3,3}
2601: {2,2,7,7}
3025: {3,3,5,5}
3267: {2,2,2,5,5}
3375: {2,2,2,3,3,3}
6075: {2,2,2,2,2,3,3}
7225: {3,3,7,7}
7803: {2,2,2,7,7}
8649: {2,2,11,11}
11979: {2,2,5,5,5}
15125: {3,3,3,5,5}
15129: {2,2,13,13}
24025: {3,3,11,11}
25947: {2,2,2,11,11}
27225: {2,2,3,3,5,5}
28125: {2,2,3,3,3,3,3}
For example, 7803 = prime(1)^3 prime(4)^2.
MATHEMATICA
Select[Range[10000], !PrimePowerQ[#]&& And@@PrimeQ/@PrimePi/@First/@FactorInteger[#]&& And@@PrimeQ/@Last/@FactorInteger[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 24 2022
STATUS
approved