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A048166 Numbers k that are divisible by the number of unitary divisors of k (A034444). 9

%I #29 Jul 16 2019 12:11:43

%S 1,2,4,8,12,16,20,24,28,32,36,40,44,48,52,56,64,68,72,76,80,88,92,96,

%T 100,104,108,112,116,120,124,128,136,144,148,152,160,164,168,172,176,

%U 184,188,192,196,200,208,212,216,224,232,236,240,244,248,256,264,268

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

%H Amiram Eldar, <a href="/A048166/b048166.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..5000 from G. C. Greubel)

%F 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

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

%t okQ[n_] := Divisible[n, DivisorSum[n, Boole[CoprimeQ[#, n/#]]&]]; Select[ Range[300], okQ] (* _Jean-François Alcover_, Dec 05 2015 *)

%t Select[Range[270], Divisible[#, 2^PrimeNu[#]] &] (* _Amiram Eldar_, Jul 16 2019 *)

%o (PARI) isok(n) = !(n % sumdiv(n, d, gcd(d, n/d)==1)); \\ _Michel Marcus_, Feb 25 2014

%o (PARI) isok(n) = !(n % 2^omega(n)); \\ _Amiram Eldar_, Jul 16 2019

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

%K nonn

%O 1,2

%A _Labos Elemer_

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)