

A255686


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).


0



3, 9, 12, 15, 18, 21, 27, 33, 39, 45, 51, 63, 69, 87, 93, 111, 123, 135, 141, 153, 159, 177, 189, 201, 219, 225, 237, 249, 255, 267, 291, 303, 309, 321, 339, 363, 381, 393, 411, 423, 453, 459, 501, 537, 543, 573, 579, 633, 669, 699
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OFFSET

1,1


COMMENTS

Number n such that A002322(A193293(n))= A002322(A193294(n)).
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, ...


LINKS

Table of n, a(n) for n=1..50.


EXAMPLE

18 is in the sequence because A002322(A193293(18)) = A002322(360) = 12 and A002322(A193294(18))= A002322(5040) = 12.


MATHEMATICA

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}]


PROG

(PARI) a002322(n) = lcm(znstar(n)[2]);
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


CROSSREFS

Cf. A000045, A002322, A193293, A193294.
Sequence in context: A073536 A077468 A089425 * A138921 A194412 A136290
Adjacent sequences: A255683 A255684 A255685 * A255687 A255688 A255689


KEYWORD

nonn


AUTHOR

Michel Lagneau, Mar 02 2015


STATUS

approved



