OFFSET
2,1
COMMENTS
A n-phile integer m is such that there are n positive integers b_1 < b_2 < ... < b_j < ... < b_n with the property that b_1 divides b_2, b_2 divides b_3, ..., b_[j-1] divides b_j, ..., b_[n-1] divides b_n, and m = b_1 + b_2 + ... + b_j + ... + b_n. A number that is not n-phile is called n-phobe.
The words 'n-phile' and 'n-phobe' come from the French website Diophante (see link).
The number of n-phobe numbers is always finite, the smallest one is always 1 and the largest n-phobe number is in A349188.
a(6) >= 176. - Michel Marcus, Nov 15 2021
a(6) >= 177, a(7) >= 459, a(8) >= 1162, a(9) >= 2947. - David A. Corneth, Nov 15 2021
Indeed, all these bounds are the corresponding values of a(6), a(7), a(8) and a(9). Proof comes from Proof link in A349188. - Bernard Schott, Nov 19 2021
LINKS
Diophante, A496 - Pentaphiles et pentaphobes (in French).
EXAMPLE
For n = 2, integers 1 and 2 are 2-phobe, then for m >= 3, every m = 1 + (m-1) with 1 < m-1 and 1 divides m-1, so, each m >= 3 is 2-phile number and a(2) = 2.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Bernard Schott, Nov 14 2021
EXTENSIONS
a(6)..a(11) from David A. Corneth, Nov 19 2021
STATUS
approved