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Pentaphobe or 5-phobe numbers: integers that are not pentaphile numbers.
4

%I #19 Nov 18 2021 03:59:31

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,28,29,30,32,33,34,35,36,37,38,40,41,42,44,48,49,50,51,52,53,54,56,

%U 60,65,66,68,72,74,80,84,97,98,102,104,108,120,132,144,168,194,240

%N Pentaphobe or 5-phobe numbers: integers that are not pentaphile numbers.

%C Pentaphile numbers are described in A348518.

%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 and the smallest one is always 1; here, there exist 68 pentaphobe numbers and the largest one is 240.

%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 5 positive integers b_1 < b_2 < b_3 < b_4 < b_5 such that b_1 divides b_2, b_2 divides b_3, b_3 divides b_4, b_4 divides b_5, and 32 = b_1 + b_2 + b_3 + b_4 + b_5, hence 32 is a term.

%o (PARI) isok(k) = forpart(p=k, if (#Set(p) == 5, if (!(p[2] % p[1]) && !(p[3] % p[2]) && !(p[4] % p[3]) && !(p[5] % p[4]), return(0))), , [5, 5]); 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), A348519 (k=4), this sequence (k=5).

%K nonn,fini,full

%O 1,2

%A _Bernard Schott_, Nov 02 2021