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Numbers n such that antisigma(n) divides Fibonacci(n).
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%I #18 May 10 2017 11:32:02

%S 3,4,8,672,720,3960,25056,114912,323928,1064880,3899880,16758000,

%T 59222400

%N Numbers n such that antisigma(n) divides Fibonacci(n).

%C a(14) > 10^9. - _Giovanni Resta_, May 06 2017

%e F(8) = 21, 8*9/2 - sigma(8) = 21 and 21/21 = 1.

%p with(numtheory): with(combinat): P:=proc(q) local n; for n from 1 to q do

%p if n*(n+1)/2-sigma(n)>0 then if type(fibonacci(n)/(n*(n+1)/2-sigma(n)), integer) then print(n); fi; fi; od; end: P(10^6);

%t Select[Range[3, 150000], Divisible[Fibonacci@ #, # (# + 1)/2 - DivisorSigma[1, #]] &] (* or *)

%t Do[If[Divisible[Fibonacci@ #, # (# + 1)/2 - DivisorSigma[1, #]] &@ n, Print@ n], {n, 3, 150000}] (* _Michael De Vlieger_, May 03 2017, both after _Robert G. Wilson v_ at A024816 *)

%Y Cf. A000045, A024816, A258748.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, May 03 2017

%E a(10)-a(12) from _Robert G. Wilson v_, May 06 2017

%E a(13) from _Giovanni Resta_, May 06 2017