login
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
OFFSET
1,2
LINKS
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.
Sequence in context: A331051 A325270 A051278 * A366318 A339424 A175127
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 06 2019
STATUS
approved