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%I #9 Mar 18 2015 06:08:00
%S 3,9,12,15,18,21,27,33,39,45,51,63,69,87,93,111,123,135,141,153,159,
%T 177,189,201,219,225,237,249,255,267,291,303,309,321,339,363,381,393,
%U 411,423,453,459,501,537,543,573,579,633,669,699
%N Numbers n such that lambda(sum of odd divisors of Fibonacci(n)) = lambda(sum of even divisors of Fibonacci(n)) where lambda is the Carmichael function (A002322).
%C Number n such that A002322(A193293(n))= A002322(A193294(n)).
%C a(n) is divisible by 3, and a majority of numbers a(n)/3 are primes: 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 47, 53, 59, 67, 73, 79, 83, 89, 97, 101, 103, 107, 113, 127, 131, 137, 151, 167, 179, 181, 191, 193, 211, 223, 233, ... The nonprimes a(n)/3 are 1, 4, 6, 9, 15, 21, 45, 51, 63, 75, 121, 153, ...
%e 18 is in the sequence because A002322(A193293(18)) = A002322(360) = 12 and A002322(A193294(18))= A002322(5040) = 12.
%t f[x_] := Plus @@ Select[Divisors[Fibonacci[x]], OddQ[#] &]; g[x_] := Plus @@ Select[Divisors[Fibonacci[x]], EvenQ[#]&];Do[If[CarmichaelLambda[f[n]]== CarmichaelLambda[g[n]],Print[n]],{n,1,500}]
%o (PARI) a002322(n) = lcm(znstar(n)[2]);
%o isok(n) = my(fn = fibonacci(n)); my(sod = sumdiv(fn, d, d*(d%2))); my(sed = sigma(fn) - sod); sod && sed && (a002322(sod) == a002322(sed)); \\ _Michel Marcus_, Mar 02 2015
%Y Cf. A000045, A002322, A193293, A193294.
%K nonn
%O 1,1
%A _Michel Lagneau_, Mar 02 2015
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