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A074845 Numbers k such that S(k) = largest difference between consecutive divisors of k (ordered by size), where S(k) is the Kempner function (A002034).

%I A074845 #31 Apr 13 2024 14:55:21
%S A074845 6,8,9,10,14,22,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,
%T A074845 158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,
%U A074845 334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514
%N A074845 Numbers k such that S(k) = largest difference between consecutive divisors of k (ordered by size), where S(k) is the Kempner function (A002034).
%C A074845 It appears that terms > 6 are simply given by: composite k such that k^2 doesn't divide A000254(k). - _Benoit Cloitre_, Mar 09 2004
%C A074845 It appears that A011776(a(k)) = 2. - _Gionata Neri_, Jul 31 2017
%C A074845 It appears that this sequence consists of the numbers k such that A045763(k) > 0 and k does not divide A070251(k). - _Isaac Saffold_, Jun 01 2018
%H A074845 Michael De Vlieger, <a href="/A074845/b074845.txt">Table of n, a(n) for n = 1..670</a> (a(n) < 10^4, from b-file at A002034).
%t A074845 Select[Range@ 514, Function[n, Module[{m = 1}, While[! Divisible[m!, n], m++]; m] == Max@ Differences@ Divisors@ n]] (* _Michael De Vlieger_, Jul 31 2017 *)
%o A074845 (PARI) K(n) = my(s=1); while(s!%n>0, s++); s;
%o A074845 dd(n) = my(vd=divisors(n)); vecmax(vector(#vd-1, k, vd[k+1] - vd[k]));
%o A074845 isok(n) = K(n) == dd(n); \\ _Michel Marcus_, Aug 03 2017
%Y A074845 Cf. A002034, A060681.
%K A074845 easy,nonn
%O A074845 1,1
%A A074845 _Jason Earls_, Sep 10 2002