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A264907 a(n) is the smallest "cyclic" integer, k, that has exactly n prime factors. 0

%I

%S 2,15,255,5865,170085,9014505,1661569239,117971415969,494390700895,

%T 42163217429333,2571956263189313,551363902358334637

%N a(n) is the smallest "cyclic" integer, k, that has exactly n prime factors.

%C The cyclic numbers are given in A003277.

%C a(n) = k if k = p_1*p_2*...*p_n where the p_i are distinct primes and no p_j-1 is divisible by any p_i and k is the smallest such integer.

%e The prime factorizations for the first 12 terms are:

%e 2

%e 3, 5

%e 3, 5, 17

%e 3, 5, 17, 23

%e 3, 5, 17, 23, 29

%e 3, 5, 17, 23, 29, 53

%e 3, 11, 17, 29, 41, 47, 53

%e 3, 11, 17, 29, 41, 47, 53, 71

%e 5, 7, 13, 17, 19, 23, 37, 59, 67

%e 7, 11, 13, 17, 19, 31, 37, 41, 47, 59

%e 7, 11, 13, 17, 19, 31, 37, 41, 47, 59, 61

%e 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 61, 71

%t (* about 45 seconds on laptop computer *)

%t f[list_] := Boole[Map[Apply[Divisible, #] &,

%t Level[Table[Table[{list[[i]] - 1, list[[j]]}, {i, j + 1, Length[list]}], {j,1, Length[list] - 1}], {2}]]]; Prepend[Map[Apply[Times, #] &,

%t Table[First[Select[Subsets[Table[Prime[n], {n, 2, 18}], {k}],

%t Total[f[#]] == 0 &]], {k, 2, 10}]], 2]

%Y Cf. A003277.

%K nonn,more

%O 1,1

%A _Geoffrey Critzer_, Nov 28 2015

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Last modified June 1 20:49 EDT 2020. Contains 334765 sequences. (Running on oeis4.)