A329730 - OEIS

%I #7 Nov 21 2019 18:10:07

%S 1,3,4,8,12,24,33,91,132,201,728,812,921,1608,1612,2064,2496,2854,

%T 3058,3240,3435,3500,4426,5074,5664,5762,6860,7318,7368,8434,9500,

%U 9846,10286,11073,12982,13773,14252,14386,17241,17246,18321,18723,18898,19628,21309,21538

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

%C The unitary version of A033632.

%H Amiram Eldar, <a href="/A329730/b329730.txt">Table of n, a(n) for n = 1..10000</a>

%e 33 is the sequence since usigma(uphi(33)) = usigma(20) = 30 and uphi(usigma(33)) = uphi(48) = 30.

%t usigma[1]=1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); aQ[n_] := usigma[uphi[n]] == uphi[usigma[n]]; Select[Range[22000], aQ]

%Y Cf. A033632, A034448, A047994.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 19 2019