A048166 Numbers k that are divisible by the number of unitary divisors of k (A034444).

1, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 64, 68, 72, 76, 80, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 136, 144, 148, 152, 160, 164, 168, 172, 176, 184, 188, 192, 196, 200, 208, 212, 216, 224, 232, 236, 240, 244, 248, 256, 264, 268

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms n = 1..5000 from G. C. Greubel)

Formula

Binomial transform of [1, 1, 1, 1, -3, 5, -7, 9, -11, 13, ...]. Binomial transform of this sequence is A048481. - Gary W. Adamson, Oct 23 2007

Example

a(81) = 392 = 2^3*7^2 has 4 unitary divisors, {1, 392, 8, 49}, and 4 divides 392.

Mathematica

okQ[n_] := Divisible[n, DivisorSum[n, Boole[CoprimeQ[#, n/#]]&]]; Select[ Range[300], okQ] (* Jean-François Alcover, Dec 05 2015 *)
Select[Range[270], Divisible[#, 2^PrimeNu[#]] &] (* Amiram Eldar, Jul 16 2019 *)

Prog

(PARI) isok(n) = !(n % sumdiv(n, d, gcd(d, n/d)==1)); \\ Michel Marcus, Feb 25 2014
(PARI) isok(n) = !(n % 2^omega(n)); \\ Amiram Eldar, Jul 16 2019

Crossrefs

Cf. A033950, A034444, A000005, A048167, A048481.

Sequence in context: A325326 A215459 A019442 * A360013 A335738 A364056

Adjacent sequences: A048163 A048164 A048165 * A048167 A048168 A048169

Keyword

nonn

Author

Labos Elemer

Status

approved