OFFSET
1,2
COMMENTS
Let gpf(m) be the greatest prime factor of m and the subset E(n) = {m, m+1, ..., m+L-1} such that gpf(m) > gpf(m+1) > ... > gpf(m+L-1) where L is the maximum length of E(n) and n the index such that {E(1) union E(2) union .... } = {2, 3, 4, ...}.
The growth of a(n) is very slow. See the following smallest values of m such that a(m) = n:
a(1) = 1, a(2) = 2, a(20) = 3, a(8) = 4, a(251) = 5, a(936) = 6, a(15553) = 7, a(6380) = 8, a(54838)=9, a(293548) = 10.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
A006530 with decreasing blocks marked: (2), (3, 2), (5, 3), (7, 2), (3), (5), (11, 3), (13, 7, 5, 2), .... Thus the terms of this sequence are 1, 2, 2, 2, 1, 1, 2, 4, ....
MAPLE
N:= 1000: # to use A006530(1..N)
L:= map(max @ numtheory:-factorset, [$1..N]):
DL:= L[2..-1]-L[1..-2]:
R:= select(t -> DL[t]>= 0, [$1..N-1]):
R[2..-1]-R[1..-2]; # Robert Israel, Mar 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 12 2012
STATUS
approved