A329856 - OEIS

%I #18 Jan 06 2020 18:10:16

%S 1,3,4,5,8,9,12,17,20,24,32,36,40,68,72,96,128,136,160,257,288,384,

%T 544,640,1028,1152,2056,2176,8192,8224,24576,32896,40960,44352,65537,

%U 73728,131072,139264,262148,393216,524288,524296,655360,1179648,1572864,2097184

%N Numbers k such that usigma(uphi(k)) = k where usigma is the sum of unitary divisors of k (A034448) and uphi is the unitary totient function (A047994).

%H Amiram Eldar, <a href="/A329856/b329856.txt">Table of n, a(n) for n = 1..74</a> (terms below 5*10^10)

%e 3 is in the sequence since usigma(uphi(3)) = usigma(2) = 3.

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); Select[Range[10^4], usigma[uphi[#]] == # &]

%Y The unitary version of A018784.

%Y Cf. A034448, A047994.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 22 2019