A074845 - OEIS

%I #31 Apr 13 2024 14:55:21

%S 6,8,9,10,14,22,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,

%T 158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,

%U 334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514

%N 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 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 It appears that A011776(a(k)) = 2. - _Gionata Neri_, Jul 31 2017

%C 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 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 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 (PARI) K(n) = my(s=1); while(s!%n>0, s++); s;

%o dd(n) = my(vd=divisors(n)); vecmax(vector(#vd-1, k, vd[k+1] - vd[k]));

%o isok(n) = K(n) == dd(n); \\ _Michel Marcus_, Aug 03 2017

%Y Cf. A002034, A060681.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Sep 10 2002