|
|
A329881
|
|
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).
|
|
1
|
|
|
4032, 13104, 58032, 69648, 237744, 278592, 365652, 1114368, 15333552, 71319552, 245364912, 981465264, 1141112832, 4564451328, 873139150710, 4020089387184
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Analogous to superperfect numbers (A019279) as nonunitary doubly perfect numbers (A064592) is analogous to perfect numbers (A000396).
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
|
|
LINKS
|
|
|
MATHEMATICA
|
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*# &]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|