A325639 Numbers n for which A091255(n, sigma(n)) = n.

1, 6, 28, 120, 312, 428, 456, 496, 504, 672, 760, 6552, 8128, 30240, 31452, 32760, 429240, 523776, 2178540, 5009850, 7505976, 23569920, 33550336, 45532800, 142990848, 186076800, 379975680

Offset: 1

Author

Antti Karttunen, May 21 2019

Keywords

• nonn
• more

Comments

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, ...

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

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

Links

• Index entries for sequences where any odd perfect numbers must occur

Crossrefs

Fixed points of A325632 and A325634.

Cf. A000203, A007691, A048720, A091255.

Cf. A000396, A325638 (subsequences).

Programs

PARI

A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
A325634(n) = A091255sq(n, sigma(n));
isA325639(n) = (A325634(n)==n);