OFFSET
1,2
COMMENTS
This sequence uses the same rules as A336957 except with the additional restriction that a(n) must have a different number of divisors than a(n-1). This leads to the terms showing a greater variation in value. For example in the first 5000 terms the maximum is a(3915) = 228569, compared to a maximum of a(3225) = 11053 for A336957 in the same range. Like A336957 is it likely all positive integers other than the prime-powers eventually appear.
EXAMPLE
a(4) = 45, as a(4) must share a factor with a(3) = 6, have a prime factor not in 6, have no common factor with a(2) = 2, and not have tau(6) = 4 divisors. The smallest positive integer satisfying these conditions is 45. Note that A336957(4) = 15, but 15 has four divisors thus cannot be chosen here.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Sep 27 2021
STATUS
approved