A361935 Numbers k such that k and k+1 are both primitive unitary abundant numbers (definition 2, A302574).

2457405145194, 2601523139214, 3320774552094, 3490250769005, 3733421997305, 3934651766045, 3954730124345, 4514767592334, 4553585751714, 4563327473705, 5226433847634

Offset: 1

Author

Amiram Eldar, Mar 31 2023

Keywords

• nonn
• more

Comments

There are no more terms below 10^13.

There are no numbers k such that k and k+1 are both unitary abundant numbers with definition 1 (A302573) below 10^13.

Crossrefs

Subsequence of A034683, A302574 and A331412.

Cf. A302573.

Similar sequences: A283418, A330872.

Programs

Mathematica

f1[p_, e_] := 1 + 1/p^e; f2[p_, e_] := p^e/(p^e + 1);
puabQ[n_] := (r = Times @@ f1 @@@ (f = FactorInteger[n])) > 2 && r * Max @@ f2 @@@ f <= 2;
Select[Import["https://oeis.org/A331412/b331412.txt", "Table"][[;; , 2]], puabQ[#] && puabQ[# + 1] &]