A133996 -id:A133996 - cp's OEIS frontend

A133997 a(n) = the smallest positive integer with exactly n positive "isolated divisors". A divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

1, 3, 9, 15, 36, 45, 126, 96, 144, 120, 324, 240, 336, 432, 360, 480, 672, 864, 720, 840, 1260, 1008, 1080, 1920, 1440, 2040, 1680, 2016, 2160, 3024, 2880, 2520, 4620, 4200, 3360, 5544, 4320, 6048, 6300, 9072, 7200, 11700, 5040, 12096, 7920, 7560, 10800

Offset: 1

Leroy Quet, Oct 01 2007

nonn

Ray Chandler, Table of n, a(n) for n=1..577

Cf. A133996, A132881.

With[{s = KeySort@ PositionIndex@ Table[1 + Count[Rest@ Divisors@ n, ?(NoneTrue[# + {-1, 1}, Divisible[n, #] &] &)], {n, 12000}]}, Function[t, TakeWhile[#, # > 0 &] &@ ReplacePart[t, Map[# -> Lookup[s, #][[1]] &, Keys@ s]]]@ ConstantArray[0, Last@ Keys@ s]] (* _Michael De Vlieger, Oct 11 2017 *)

Extended by Ray Chandler, Jun 24 2008

A134000 Array read by antidiagonals: row n contains the positive integers each with exactly n positive "non-isolated divisors". A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

Original entry on oeis.org

2, 6, 4, 12, 18, 8, 30, 20, 54, 10, 60, 42, 24, 66, 14, 90, 72, 126, 36, 78, 16, 180, 168, 84, 150, 40, 102, 22, 360, 210, 270, 120, 294, 48, 114, 26, 630, 660, 240, 330, 132, 306, 56, 138, 28, 420, 924, 1080, 480, 336, 144, 342, 80, 162, 32, 840, 720, 1200, 1092, 504

Offset: 2

Leroy Quet, Oct 01 2007

The left column (column 1) of the array is sequence A133996. This array written as a sequence is a permutation of the even positive integers. The array starts at column 1 and row 2. (There are no integers with exactly 1 non-isolated divisor.)

			2 non-isolated divisors: 2, 4, 8, 10, 14, ...
3 non-isolated divisors: 6, 18, 54, 66, ...
4 non-isolated divisors: 12, 20, 24, ...
etc.

Cf. A134001, A133996.

Extended by Ray Chandler, Jun 25 2008

cp's OEIS Frontend

A133997 a(n) = the smallest positive integer with exactly n positive "isolated divisors". A divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

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