cp's OEIS Frontend

The number 88978489594 is the 45th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 95 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).

The number 95186291194 is the 46th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 112 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k > 1 such that the number of preimages of an even number n is O((log n)^k).

The number 666304038394 is the 48th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 130 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).

The number 690100611194 is the 49th term of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function. Up to 2^40, this is the even number with the greatest number of preimages. As of May 22 2017, this is the largest known even number with the greatest number of preimages.

There are exactly 139 terms in the sequence.

In 2016, C. Pomerance proved that, for every e > 0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).

The number 289697407994 is the 47th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 123 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).

The number 57939481594 is the 44th element of A283157. That is, no even number below it has more preimages under the sum-of-proper-divisors function.

There are exactly 94 elements in the sequence.

In 2016, C. Pomerance proved that, for every e>0, the number of preimages is O_e(n^{2/3+e}).

Conjecture: there exists a positive real number k such that the number of preimages of an even number n is O((log n)^k).