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).

6, 8, 9, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514

Offset: 1

Author

Jason Earls, Sep 10 2002

Keywords

• easy
• nonn

Comments

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

It appears that A011776(a(k)) = 2. - Gionata Neri, Jul 31 2017

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..670 (a(n) < 10^4, from b-file at A002034).

Crossrefs

Cf. A002034, A060681.

Programs

Mathematica

Select[Range@ 514, Function[n, Module[{m = 1}, While[! Divisible[m!, n], m++]; m] == Max@ Differences@ Divisors@ n]] (* Michael De Vlieger, Jul 31 2017 *)

PARI

K(n) = my(s=1); while(s!%n>0, s++); s;
dd(n) = my(vd=divisors(n)); vecmax(vector(#vd-1, k, vd[k+1] - vd[k]));
isok(n) = K(n) == dd(n); \\ Michel Marcus, Aug 03 2017