A063891 - OEIS

%I #20 Apr 10 2019 13:43:20

%S 1631,2016,8928,11808,36576,45360,1486080,2359008,3093552,37748448,

%T 101350656,150994656,2885670144

%N Numbers k such that nusigma(usigma(k)) = 2k, where usigma(k) is the sum of unitary divisors of k (A034448) and nusigma(k) is the sum of non-unitary divisors of k (A048146).

%C a(14) > 2*10^11. All the numbers of the form 2^5 * 3^2 * p where p>3 is a  Mersenne prime (A000668) are in the sequence, so a(14) <= 618475290336. - _Giovanni Resta_, Apr 10 2019

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1,n] - usigma[n]; Select[Range[12000], nusigma[usigma[#]] == 2# &] (* _Amiram Eldar_, Apr 10 2019 *)

%o (PARI) u(n) = sumdiv(n,d, if(gcd(d,n/d)==1,d));

%o z(n)=sigma(n)-u(n) ;

%o for(n=1,10^8, if(z(u(n))==2*n,print1(n, ", ")))

%Y Cf. A000203, A034448, A048146, A019284, A063885.

%K more,nonn

%O 1,1

%A _Jason Earls_, Aug 28 2001

%E More terms from _Thomas Baruchel_, Oct 22 2003

%E a(11)-a(13) from _Amiram Eldar_, Apr 10 2019