OFFSET
1,10
COMMENTS
The powers of primes correspond to A000961.
Apparently, a(n) >= 0 for any n > 0.
For a given number n, while iterating A070229, we may encounter several prime increments (=several greatest prime factors). It is likely that the number of distinct increments before reaching a power of a prime is not bounded.
For k = 0..9, the least numbers with k distinct increments are:
k n Increments
- ------ ------------------------------------------
0 1 {}
1 6 {3}
2 12 {3, 5}
3 72 {3, 5, 17}
4 135 {5, 7, 11, 17}
5 686 {7, 11, 13, 19, 41}
6 12408 {47, 53, 59, 71, 89, 149}
7 35378 {19, 23, 67, 89, 101, 179, 211}
8 127581 {43, 53, 73, 103, 113, 227, 283, 457}
9 222111 {37, 79, 97, 191, 233, 239, 311, 359, 631}
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 0 iff n belongs to A000961.
EXAMPLE
PROG
(PARI) a(n) = for (k=0, oo, if (omega(n) <= 1, return (k), my (f=factor(n)); n += f[#f~, 1]))
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Jan 05 2019
STATUS
approved