OFFSET
1,2
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) = 1/Product_{k>=0} (1 - 1/prime(2^k)) = 3.81625872357742992578... . - Amiram Eldar, Dec 03 2022
EXAMPLE
The sequence of all integer partitions whose parts are all powers of 2 (including 1) begins: (), (1), (2), (11), (21), (4), (111), (22), (211), (41), (1111), (221), (8), (42), (2111), (222), (411), (11111), (2211), (81), (421), (21111), (44).
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
pow2Q[n_]:=Or[n==1, MatchQ[FactorInteger[n], {{2, _}}]];
Select[Range[100], And@@pow2Q/@primeMS[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 16 2018
STATUS
approved