%I #15 Nov 24 2019 14:35:09

%S 4032,13104,58032,69648,237744,278592,365652,1114368,15333552,

%T 71319552,245364912,981465264,1141112832,4564451328,873139150710,

%U 4020089387184

%N Nonunitary doubly superperfect numbers: numbers k such that nusigma(nusigma(k)) = 2*k, where nusigma(k) = sigma(k) - usigma(k) is the sum of nonunitary divisors of k (A048146).

%C Analogous to superperfect numbers (A019279) as nonunitary doubly perfect numbers (A064592) is analogous to perfect numbers (A000396).

%C If n = 2^k*3*1451 and nusigma(n) = 2^5*3*11^2*p, with p > 11 prime, then n is a term. This happens for k = 4, 6, 8, 14, 18, 20, 32, 62, 90, 108, 128, 522, 608, ... . Similarly, if p=2^k-1 is prime (A000043), then 2^4*3^2*13*p is a term for k > 2. - _Giovanni Resta_, Nov 23 2019

%C a(17) > 6*10^12. - _Giovanni Resta_, Nov 24 2019

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; Select[Range[3*10^5], nusigma[nusigma[#]] == 2*# &]

%Y Cf. A000396, A019279, A034448, A038843, A048146, A064592, A328120, A329884.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Nov 23 2019

%E a(15)-a(16) from _Giovanni Resta_, Nov 24 2019