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A067947 Numbers k such that k divides 7^k - 1.

%I A067947 #32 Jan 22 2025 19:52:55
%S A067947 1,2,3,4,6,8,9,12,16,18,20,24,27,32,36,40,48,54,57,60,64,72,80,81,96,
%T A067947 100,108,114,120,128,144,156,160,162,171,180,192,200,216,220,228,240,
%U A067947 243,256,258,272,288,300,312,320,324,333,342,360,384,400,432,440,456
%N A067947 Numbers k such that k divides 7^k - 1.
%C A067947 For k >= 0, 2^k is in the sequence.
%C A067947 From _Alexander Adamchuk_, Jan 05 2007: (Start)
%C A067947 3^k is in the sequence.
%C A067947 k! is in the sequence for k < 7.
%C A067947 k!/7 is in the sequence for 7 <= k < 14.
%C A067947 k!/7^2 is in the sequence for 14 <= k < 21.
%C A067947 k!/7^3 is in the sequence for 21 <= k < 28.
%C A067947 k!/7^4 is in the sequence for k = 28. (End)
%H A067947 Seiichi Manyama, <a href="/A067947/b067947.txt">Table of n, a(n) for n = 1..10000</a>
%t A067947 Select[Range[600], Divisible[7^# - 1, #] &] (* _Vincenzo Librandi_, Apr 24 2017 *)
%t A067947 Join[{1},Select[Range[500],PowerMod[7,#,#]==1&]] (* _Harvey P. Dale_, Jan 22 2025 *)
%o A067947 (PARI) is(n)=Mod(7,n)^n==1 \\ _Charles R Greathouse IV_, Nov 04 2016
%o A067947 (Magma) [n: n in [1..500] | (7^n-1) mod n eq 0 ]; // _Vincenzo Librandi_, Apr 24 2017
%Y A067947 Cf. A127107 (k^2 divides 7^k - 1).
%K A067947 easy,nonn
%O A067947 1,2
%A A067947 _Benoit Cloitre_, Mar 05 2002