OFFSET
1,1
COMMENTS
A002827 is a subset of this sequence.
No more terms below 10^8. - Amiram Eldar, Jan 12 2019
LINKS
Eric Weisstein's World of Mathematics, Unitary Divisor
Eric Weisstein's World of Mathematics, Unitary Divisor Function
Eric Weisstein's World of Mathematics, Unitary Perfect Number
Wikipedia, Unitary divisor
EXAMPLE
Divisors of 85 are 1, 5, 17, 85. Unitary aliquot parts are 1, 5, 17.
We have:
1 + 5 + 17 = 23;
5 + 17 + 23 = 45;
17 + 23 + 45 = 85.
Divisors of 2009 are 1, 7, 41, 49, 287, 2009.
Unitary aliquot parts are 1, 41, 49. We have:
1 + 41 + 49 = 91;
41 + 49 + 91 = 181;
49 + 91 + 181 = 321;
91 + 181 + 321 = 593;
181 + 321 + 593 = 1095;
321 + 593 + 1095 = 2009.
MAPLE
with(numtheory):P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do if not isprime(n) then b:=sort([op(divisors(n))]); a:=[];
for k from 1 to nops(b)-1 do if gcd(b[k], n/b[k])=1 then a:=[op(a), b[k]]; fi; od;
a:=sort(a); b:=nops(a); if b>1 then for k from 1 to b do v[k]:=a[k]; od;
t:=b+1; v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1);
od; if v[t]=n then print(n); fi; fi; fi; od; end: P(10^9, 10000);
MATHEMATICA
aQ[n_] := Module[{s = Most[Select[Divisors[n], GCD[#, n/#] == 1 &]]}, If[Length[s] == 1, False, While[Total[s] < n, AppendTo[s, Total[s]]; s = Rest[s]]; Total[s] == n]]; Select[Range[2, 10^8], aQ] (* Amiram Eldar, Jan 12 2019 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, May 22 2015
EXTENSIONS
a(11)-a(12) from Amiram Eldar, Jan 12 2019
STATUS
approved