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%I #28 Nov 19 2021 16:42:19
%S 2,9,23,68,177,459,1162,2947,7306,18202
%N Number of n-phobe numbers.
%C 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.
%C The words 'n-phile' and 'n-phobe' come from the French website Diophante (see link).
%C The number of n-phobe numbers is always finite, the smallest one is always 1 and the largest n-phobe number is in A349188.
%C a(6) >= 176. - _Michel Marcus_, Nov 15 2021
%C a(6) >= 177, a(7) >= 459, a(8) >= 1162, a(9) >= 2947. - _David A. Corneth_, Nov 15 2021
%C 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
%H Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a4-equations-diophantiennes/3143-a496-pentaphiles-et-pentaphobes">A496 - Pentaphiles et pentaphobes</a> (in French).
%e 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.
%Y k-phile numbers: A160811 \ {5} (k=3), A348517 (k=4), A348518 (k=5).
%Y k-phobe numbers: A019532 (k=3), A348519 (k=4), A348520 (k=5).
%Y Cf. A349188.
%K nonn,more
%O 2,1
%A _Bernard Schott_, Nov 14 2021
%E a(6)..a(11) from _David A. Corneth_, Nov 19 2021