A066664 Composite numbers n whose divisors less than or equal to sqrt(n) are consecutive, from 1 up to some number k.

4, 6, 8, 10, 12, 14, 18, 22, 24, 26, 34, 38, 46, 58, 60, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478

Offset

1,1

Comments

The sequence consists of all numbers of the form 2p with p prime, along with 8, 12, 18, 24 and 60. See sketch of proof in A066522.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Mathematica

a = {}; Do[ If[ !PrimeQ[n], k = Select[ Divisors[n], # <= Sqrt[n] &]; If[ Last[k] == Length[k], a = Append[a, n]]], {n, 1, 500} ]; a
dQ[n_]:=!PrimeQ[n]&&Union[Differences[Select[Divisors[n], #<=Sqrt[n]&]]] == {1}; Select[Range[500], dQ] (* Harvey P. Dale, Nov 06 2013 *)

Prog

(Haskell)
a066664 n = a066664_list !! (n-1)
a066664_list = filter ((== 0) . a010051) $ tail a066522_list
-- Reinhard Zumkeller, Nov 14 2011

Crossrefs

These are the composite members of A066522: intersection of A002808 and A066522.

Subsequence: A100484.

Sequence in context: A258036 A242396 A061344 * A064938 A050990 A289425

Adjacent sequences: A066661 A066662 A066663 * A066665 A066666 A066667

Keyword

nice,nonn,easy

Author

Robert G. Wilson v, Jan 07 2002

Status

approved