Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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