A248881 - OEIS

A248881

Numbers n such that lambda(sum of even divisors of 2n) = lambda(sum of odd divisors of 2n) where lambda is the Carmichael function (A002322).

1, 3, 5, 6, 9, 11, 13, 17, 18, 19, 25, 26, 27, 29, 36, 37, 38, 41, 43, 45, 49, 50, 53, 54, 59, 61, 63, 65, 67, 68, 72, 73, 74, 75, 81, 82, 83, 85, 86, 87, 89, 90, 95, 97, 98, 99, 100, 101, 103, 107, 109, 113, 117, 121, 122, 125, 126, 130, 131, 134, 137, 139

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OFFSET

1,2

COMMENTS

Number n such that A002322(A074400(n))= A002322(A000593(n)).

The squares of the form p^2 with p prime are in the sequence because the divisors of 2p^2 are {1,2,p,2p,p^2,2p^2} => sum of even divisors s0 = 2+2p+2p^2 = 2(p^2+p+p^2) and sum of odd divisors s1 = 1+p+p^2 and lambda(s0) = lambda(s1) = lambda(2*s0).

A majority of primes are in the sequence: 3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, ... but the primes 7, 23, 31, 47, 71, 79, 127, 151, 167, 191, 223, 239, 263, 367, 383, 431, ... are not in the sequence.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

18 is in the sequence because A002322(A074400(18))= A002322(78)= 12 and because A002322(A000593(18)) = A002322(13) = 12.

MATHEMATICA

lst={}; f[x_] := Plus @@ Select[Divisors[x], OddQ[#] &]; g[x_] := Plus @@ Select[Divisors[x], EvenQ[#]&]; Do[If[CarmichaelLambda[f[n]]== CarmichaelLambda[g[n]], AppendTo[lst, n/2]], {n, 1, 500}]; lst

PROG

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

isok(n) = my(sod = sumdiv(2*n, d, d*(d%2))); my(sed = sigma(2*n) - sod); sod && sed && (a002322(sod) == a002322(sed)); \\ Michel Marcus, Mar 07 2015

CROSSREFS

Cf. A000593, A002322, A074400, A077591.

Sequence in context: A047445 A341349 A248638 * A205534 A323115 A285377

Adjacent sequences: A248878 A248879 A248880 * A248882 A248883 A248884

KEYWORD

nonn,changed

AUTHOR

Michel Lagneau, Mar 05 2015

STATUS

approved