|
|
A191581
|
|
Numbers whose sum of their anti-divisors divides the sum of their divisors.
|
|
2
|
|
|
3, 6, 11, 22, 30, 33, 65, 82, 117, 218, 354, 483, 508, 537, 3276, 6430, 21541, 117818, 130356, 753612, 1007328, 2113416, 2379540, 3589646, 7231219, 7346148, 8515767, 13050345, 20199648, 34424166, 44575896, 47245905, 50414595, 104335023, 217728002, 1217532421
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
A161917 is a subsequence of this sequence.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
6-> sum divisors=sigma(6)=12; sum anti-divisors=4; 12/4=3.
30-> sum divisors=sigma(30)=72; sum anti-divisors=4+12+20=36; 72/36=2.
|
|
MAPLE
|
with(numtheory): P:=proc(i) local a, b, j, k, s, n;
for n from 3 to i do b:=divisors(n); s:=add(b[k], k=1..nops(b));
k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
if type(s/a, integer) then print(n); fi; od; end: P(10^6);
|
|
MATHEMATICA
|
f[n_] := Total@ Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Range[3, 10^3], Mod[DivisorSigma[1, #], f@ #] == 0 &] (* Michael De Vlieger, Oct 08 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|