A177807
Numbers k that divide 17^k - 1.
Original entry on oeis.org
1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 42, 48, 54, 60, 64, 72, 78, 80, 84, 96, 100, 108, 116, 120, 126, 128, 144, 156, 160, 162, 168, 180, 192, 200, 216, 220, 232, 234, 240, 252, 256, 288, 294, 300, 312, 320, 324, 336, 342, 348, 360, 378, 384, 400, 420
Offset: 1
Cf.
A014960,
A014956,
A014957,
A014951,
A014949,
A014946,
A014945,
A067945,
A128358,
A128360,
A177805.
-
{1}~Join~Select[Range[420], PowerMod[17, #, #] == 1 &] (* Giovanni Resta, Jan 30 2020 *)
A333432
A(n,k) is the n-th number m that divides k^m - 1 (or 0 if m does not exist); square array A(n,k), n>=1, k>=1, read by antidiagonals.
Original entry on oeis.org
1, 1, 2, 1, 0, 3, 1, 2, 0, 4, 1, 3, 4, 0, 5, 1, 2, 9, 8, 0, 6, 1, 5, 4, 21, 16, 0, 7, 1, 2, 25, 6, 27, 20, 0, 8, 1, 7, 3, 125, 8, 63, 32, 0, 9, 1, 2, 49, 4, 625, 12, 81, 40, 0, 10, 1, 3, 4, 343, 6, 1555, 16, 147, 64, 0, 11, 1, 2, 9, 8, 889, 8, 3125, 18, 171, 80, 0, 12
Offset: 1
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 0, 2, 3, 2, 5, 2, 7, 2, ...
3, 0, 4, 9, 4, 25, 3, 49, 4, ...
4, 0, 8, 21, 6, 125, 4, 343, 8, ...
5, 0, 16, 27, 8, 625, 6, 889, 10, ...
6, 0, 20, 63, 12, 1555, 8, 2359, 16, ...
7, 0, 32, 81, 16, 3125, 9, 2401, 20, ...
8, 0, 40, 147, 18, 7775, 12, 6223, 32, ...
9, 0, 64, 171, 24, 15625, 16, 16513, 40, ...
Columns k=1-20 give:
A000027,
A063524,
A067945,
A014945,
A067946,
A014946,
A067947,
A014949,
A068382,
A014950,
A068383,
A014951,
A116621,
A177805,
A014957,
A177807,
A128358,
A333506,
A128360.
-
A:= proc() local h, p; p:= proc() [1] end;
proc(n, k) if k=2 then `if`(n=1, 1, 0) else
while nops(p(k)) 1 do od;
p(k):= [p(k)[], h]
od; p(k)[n] fi
end
end():
seq(seq(A(n, 1+d-n), n=1..d), d=1..12); # Alois P. Heinz, Mar 24 2020
-
A[n_, k_] := Module[{h, p}, p[_] = {1}; If[k == 2, If[n == 1, 1, 0], While[ Length[p[k]] < n, For[h = 1 + p[k][[-1]], Mod[k^h, h] != 1, h++]; p[k] = Append[p[k], h]]; p[k][[n]]]];
Table[A[n, 1+d-n], {d, 1, 12}, {n, 1, d}] // Flatten (* Jean-François Alcover, Nov 01 2020, after Alois P. Heinz *)
A014959
Integers k such that k divides 22^k - 1.
Original entry on oeis.org
1, 3, 7, 9, 21, 27, 39, 49, 63, 81, 117, 147, 189, 243, 273, 343, 351, 441, 507, 567, 729, 819, 1029, 1053, 1143, 1323, 1521, 1701, 1911, 2187, 2401, 2457, 2943, 3081, 3087, 3159, 3429, 3549, 3969, 4401, 4563, 5103, 5733, 6561, 6591, 7203, 7371
Offset: 1
Integers n such that n divides b^n - 1:
A067945 (b=3),
A014945 (b=4),
A067946 (b=5),
A014946 (b=6),
A067947 (b=7),
A014949 (b=8),
A068382 (b=9),
A014950 (b=10),
A068383 (b=11),
A014951 (b=12),
A116621 (b=13),
A014956 (b=14),
A177805 (b=15),
A014957 (b=16),
A177807 (b=17),
A128358 (b=18),
A125000 (b=19),
A128360 (b=20),
A014960 (b=24).
-
nxt[{n_,s_}]:={n+1,s+(n+1)*22^n}; Transpose[Select[NestList[nxt,{1,1},7500], Divisible[ Last[#],First[#]]&]][[1]] (* Harvey P. Dale, Jan 27 2015 *)
A115976
Numbers k that divide 2^(k-2) + 1.
Original entry on oeis.org
1, 3, 49737, 717027, 9723611, 21335267, 32390921, 38999627, 43091897, 86071337, 101848553, 102361457, 228911411, 302948067, 370219467, 393664027, 455781089, 483464027, 1040406177, 1272206987, 2371678553, 2571052241, 2648052857, 3054713937, 3597613307, 3782971499, 3917903851, 4005163577, 5419912241
Offset: 1
Cf.
A006521,
A006517,
A069927,
A067945,
A067946,
A067947,
A068382,
A068383,
A014945,
A014946,
A014949,
A092028.
-
lst = {}; Do[ If[ PowerMod[2, 2n - 3, 2n - 1] == 2n - 2, AppendTo[lst, 2n - 1]], {n, 10^9}]; lst (* Robert G. Wilson v, Apr 04 2006 *)
A014962
Odd numbers k that divide 25^k - 1.
Original entry on oeis.org
1, 3, 9, 21, 27, 63, 81, 93, 147, 171, 189, 243, 279, 441, 513, 567, 609, 651, 729, 837, 903, 1029, 1197, 1323, 1539, 1701, 1827, 1953, 2187, 2511, 2667, 2709, 2883, 2943, 3087, 3249, 3591, 3969, 4263, 4401, 4557, 4617, 5103, 5301, 5481, 5859, 6321
Offset: 1
Cf.
A014943,
A014945,
A014946,
A014949,
A014950,
A014951,
A014956,
A014957,
A128358,
A128360,
A014959,
A014960.
-
select(t -> 25 &^ t - 1 mod t = 0, [seq(i,i=1..10^4,2)]); # Robert Israel, Oct 04 2020
Comments