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

Author

Robert G. Wilson v, Jan 07 2002

Keywords

• nice
• nonn
• easy

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

Crossrefs

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

Subsequence: A100484.

Programs

Haskell

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

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 *)