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A218341
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Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(29) listed in ascending order.
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4
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1, 2, 4, 7, 14, 28, 3, 5, 6, 8, 10, 12, 15, 20, 21, 24, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840, 13, 26, 52, 67, 91, 134, 182, 268, 364, 469, 871, 938, 1742, 1876, 3484, 6097, 12194, 24388, 16, 48, 80, 112, 240, 336, 421, 560
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n,k) = k-th smallest element of M(n) = {d : d|(29^n-1)} \ U(n-1) with U(n) = M(n) union U(n-1) if n>0, U(0) = {}.
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EXAMPLE
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Triangle begins:
: 1, 2, 4, 7, 14, 28;
: 3, 5, 6, 8, 10, 12, 15, ...
: 13, 26, 52, 67, 91, 134, 182, ...
: 16, 48, 80, 112, 240, 336, 421, ...
: 732541, 1465082, 2930164, 5127787, 10255574, 20511148;
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MAPLE
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with(numtheory):
M:= proc(n) M(n):= divisors(29^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
T:= n-> sort([M(n)[]])[]:
seq(T(n), n=1..5);
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MATHEMATICA
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M[n_] := M[n] = Divisors[29^n-1] ~Complement~ U[n-1];
U[n_] := U[n] = If[n == 0, {}, M[n] ~Union~ U[n-1]];
T[n_] := Sort[M[n]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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