%I #21 Nov 15 2021 11:10:26

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,20,24,25,26,32,48

%N Tetraphobe or 4-phobe numbers: integers that are not tetraphile numbers.

%C Tetraphile numbers are described in A348517.

%C The idea for this sequence comes from the French website Diophante (see link).

%C It is possible to generalize for "k-phile" or "k-phobe" numbers (see Crossrefs).

%C The set of k-phobe numbers is always finite, the smallest one is always 1; here, there exist 23 tetraphobe numbers and the largest one is 48.

%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 There are no 4 positive integers b_1 < b_2 < b_3 < b_4 such that b_1 divides b_2, b_2 divides b_3, b_3 divides b_4, and 17 = b_1 + b_2 + b_3 + b_4, hence 17 is a term.

%t Select[Range@48,Select[Select[IntegerPartitions[#,{4}],Length@Union@#==4&],And@@(IntegerQ/@Divide@@@Partition[#,2,1])&]=={}&] (* _Giorgos Kalogeropoulos_, Oct 24 2021 *)

%o (PARI) isok(k) = forpart(p=k, if (#Set(p) == 4, if (!(p[2] % p[1]) && !(p[3] % p[2]) && !(p[4] % p[3]), return(0))), , [4, 4]); return(1); \\ _Michel Marcus_, Nov 14 2021

%Y k-phile numbers: A160811 \ {5} (k=3), A348517 (k=4), A348518 (k=5).

%Y k-phobe numbers: A019532 (k=3), this sequence (k=4), A348520 (k=5).

%K nonn,fini,full

%O 1,2

%A _Bernard Schott_, Oct 23 2021