A325639 - OEIS

%I #17 Jun 17 2019 18:01:50

%S 1,6,28,120,312,428,456,496,504,672,760,6552,8128,30240,31452,32760,

%T 429240,523776,2178540,5009850,7505976,23569920,33550336,45532800,

%U 142990848,186076800,379975680

%N Numbers n for which A091255(n, sigma(n)) = n.

%C Numbers n for which A000203(n) = A048720(n, k) for some k. The value of k for the initial terms is: 1, 2, 2, 7, 3, 3, 6, 2, 5, 3, 3, 6, 2, 4, 6, 4, 6, 7, 4, 3, 6, 4, 2, 4, 4, 7, 7, ...

%C Conjecture: all terms after the initial one are even. If this is true, then there are no odd perfect numbers.

%C A007691(11) = 2178540 is the first term of A007691 which is not present in this sequence.

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%o (PARI)

%o A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);

%o A325634(n) = A091255sq(n, sigma(n));

%o isA325639(n) = (A325634(n)==n);

%Y Fixed points of A325632 and A325634.

%Y Cf. A000203, A007691, A048720, A091255.

%Y Cf. A000396, A325638 (subsequences).

%K nonn,more

%O 1,2

%A _Antti Karttunen_, May 21 2019