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Numbers k such that k^2 divides 17^k-1.
18

%I #14 May 21 2024 01:14:24

%S 1,2,4,6,8,12,16,18,20,24,36,40,42,48,60,72,78,80,84,116,120,126,144,

%T 156,168,180,220,232,234,240,252,312,336,342,348,360,420,440,464,468,

%U 504,546,580,624,660,684,696,720,780,840,880,936,1008,1044,1092,1160

%N Numbers k such that k^2 divides 17^k-1.

%C The first 9 numbers (and many more) which are a multiple of their digital sum in all bases from 2 through 16 (A218087), are members of this sequence, and also of A177917. - _M. F. Hasler_, Oct 22 2012

%H Amiram Eldar, <a href="/A128397/b128397.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) is_A128397(n)=Mod(17,n^2)^n==1 \\ _M. F. Hasler_, Oct 22 2012

%Y Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

%Y Cf. A177917.

%K nonn,less

%O 1,2

%A _Alexander Adamchuk_, Mar 01 2007