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 A328028 Nonprime numbers n whose proper divisors (greater than 1 and less than n) have no consecutive divisibilities. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MAPLE 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: select(filter, [\$1..300]); # Robert Israel, Oct 11 2019 MATHEMATICA Select[Range[100], !PrimeQ[#]&&!MatchQ[DeleteCases[Divisors[#], 1|#], {___, x_, y_, ___}/; Divisible[y, x]]&] CROSSREFS Positions of 0's or 2's in A328026. 1 and positions of 1's in A328194. The version including primes is A328161. Partitions with no consecutive divisibilities are A328171. Numbers whose proper divisors have no consecutive successions are A088725. Contains A001358. Cf. A000005, A060680, A060775, A067513, A163870, A328162, A328189. Sequence in context: A331051 A325270 A051278 * A175127 A174166 A171401 Adjacent sequences:  A328025 A328026 A328027 * A328029 A328030 A328031 KEYWORD nonn AUTHOR Gus Wiseman, Oct 06 2019 STATUS approved

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Last modified February 20 07:41 EST 2020. Contains 332069 sequences. (Running on oeis4.)