OFFSET
1,1
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein, Unitary Divisor.
EXAMPLE
The third integer which is an odd unitary abundant number but is not an ordinary, squarefree abundant number is 416955. Hence a(3)=416955.
MATHEMATICA
UnitaryDivisors[ n_Integer?Positive ] := Select[ Divisors[ n ], GCD[ #, n/# ] == 1 & ]; sstar[ n_ ] := Plus @@ UnitaryDivisors[ n ] - n; UnitaryAbundantNumberQ[ k_ ] := If[ sstar[ k ] > k, True, False ]; data1 = Select[ Range[ 1, 10^7, 2 ], UnitaryAbundantNumberQ[ # ] & ]; data2 = Select[ Range[ 1, 10^7, 2 ], DivisorSigma[ 1, # ] - 2 # > 0 && ! MoebiusMu[ # ] == 0 & ]; Complement[ data1, data2 ]
uaQ[n_] := Module[{f = FactorInteger[n]}, Max[f[[;; , 2]]] > 1 && Times@@(1 + Power @@@ f) > 2n]; Select[Range[3, 2*10^6, 2], uaQ] (* Amiram Eldar, May 13 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ant King, Apr 17 2007
EXTENSIONS
More terms from Amiram Eldar, May 13 2019
STATUS
approved