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A348086
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Variation of the EKG sequence A064413: a(n) is the smallest number not already used which shares a factor with a(n-1) and has a different number of divisors than a(n-1).
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4
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1, 2, 4, 6, 3, 9, 12, 8, 16, 10, 5, 15, 18, 14, 7, 21, 24, 20, 22, 11, 33, 30, 25, 35, 28, 26, 13, 39, 36, 27, 42, 32, 34, 17, 51, 45, 40, 38, 19, 57, 48, 44, 46, 23, 69, 54, 50, 55, 60, 52, 56, 49, 63, 66, 58, 29, 87, 72, 62, 31, 93, 75, 65, 70, 64, 68, 74, 37, 111, 78, 76, 80, 82, 41, 123, 81
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OFFSET
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1,2
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COMMENTS
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This sequence uses the same rules as A064413 except with the additional restriction that a(n) must have a different number of divisors than a(n-1). Despite this additional restriction the overall behavior of the sequence is almost identical to A064413, with most values appearing only a few places away from their position in A064413.
The fixed points below 10000 are 1, 2, 8, 10, 14, 26, 32, 38, 259. It is likely no more exist.
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LINKS
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EXAMPLE
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a(9) = 16 as a(8) = 8 which shares a factor with 16, 16 is unused, and tau(8) = 4 does not equal tau(16) = 5. This is the first term that differs from A064413, the later having a(9) = 10, but tau(10) = 4 = tau(8) so is forbidden here.
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MATHEMATICA
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a[1]=1; a[2]=2; a[n_]:=a[n]=(k=1; While[GCD[k, a[n-1]]==1||SameQ@@DivisorSigma[0, {k, a[n-1]}]||MemberQ[Array[a, n-1], k], k++]; k); Array[a, 76] (* Giorgos Kalogeropoulos, Oct 08 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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