A331412 Unitary abundant numbers k such that k + 1 is also unitary abundant.

8857357509, 10783550414, 15197873690, 23620285689, 25537083494, 34736070369, 60326914934, 64139567205, 73969772954, 75776483145, 77509981185, 83968675790, 93092467754, 100012014465, 112236593469, 113606741534, 116519300534, 118905484334, 132584489114, 134889106065

Offset

1,1

Comments

Apparently most of the terms are squarefree. Up to 10^13 there are 1150 terms, for only 17 terms k either k or k + 1 is nonsquarefree, and there are no terms k such that both k and k + 1 are nonsquarefree. The first nonsquarefree term is a(32) = 285491549265.

Links

Giovanni Resta, Table of n, a(n) for n = 1..1150 (terms below 10^13)

Example

8857357509 is a term since usigma(8857357509) = 17766604800 > 2 * 8857357509, and usigma(8857357510) = 17851083264 > 2 * 8857357510, where usigma is the sum of unitary divisors function (A034448).

Crossrefs

Cf. A034448, A034683, A292704.

Analogous sequences: A096399 (regular abundant), A283418 (primitive), A318167 (bi-unitary), A327635 (infinitary), A327942 (nonunitary).

Sequence in context: A185429 A154876 A270612 * A204407 A144651 A345863

Adjacent sequences: A331409 A331410 A331411 * A331413 A331414 A331415

Keyword

nonn

Author

Amiram Eldar and Giovanni Resta, Jan 18 2020

Status

approved