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A328028
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Nonprime numbers n whose proper divisors (greater than 1 and less than n) have no consecutive divisibilities.
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14
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1, 4, 6, 9, 10, 12, 14, 15, 21, 22, 24, 25, 26, 30, 33, 34, 35, 36, 38, 39, 45, 46, 48, 49, 51, 55, 57, 58, 60, 62, 63, 65, 69, 70, 72, 74, 77, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 96, 105, 106, 108, 111, 115, 118, 119, 120, 121, 122, 123, 129, 132, 133, 134
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OFFSET
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1,2
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LINKS
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EXAMPLE
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The proper divisors of 18 are {2, 3, 6, 9}, and {3, 6} are a consecutive divisible pair, so 18 does not belong to the sequence.
The proper divisors of 60 are {2, 3, 4, 5, 6, 10, 12, 15, 20, 30}, and none of {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 10}, {10, 12}, {12, 15}, {15, 20}, or {20, 30} are divisible pairs, so 60 belongs to the sequence.
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MAPLE
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filter:= proc(n) local D, i;
if isprime(n) then return false fi;
D:= sort(convert(numtheory:-divisors(n) minus {1, n}, list));
for i from 1 to nops(D)-1 do if (D[i+1]/D[i])::integer then return false fi od:
true
end proc:
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MATHEMATICA
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Select[Range[100], !PrimeQ[#]&&!MatchQ[DeleteCases[Divisors[#], 1|#], {___, x_, y_, ___}/; Divisible[y, x]]&]
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CROSSREFS
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Positions of 0's or 2's in A328026.
The version including primes is A328161.
Partitions with no consecutive divisibilities are A328171.
Numbers whose proper divisors have no consecutive successions are A088725.
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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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