A293618 Numbers n that equal the sum of their first k consecutive aliquot bi-unitary divisors, but not all of them (i.e k < A286324(n)-1).

24, 360, 432, 1344, 2016, 19440, 45360, 68544, 714240, 864000, 1468800, 1571328, 1900800, 2391120, 2888704, 3057600, 4586400, 5241600, 103194000

Offset

1,1

Comments

The bi-unitary version of Erdős-Nicolas numbers (A194472).

If all the aliquot bi-unitary divisors are permitted (i.e. k <= A286324(n)-1), then the 3 bi-unitary perfect numbers, 6, 60 and 90, are included.

Links

Table of n, a(n) for n=1..19.

Example

24 is in the sequence since its aliquot bi-unitary divisors are 1, 2, 3, 4, 6, 8, 12 and 24 and 1 + 2 + 3 + 4 + 6 + 8 = 24.

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[bdiv[n], -2]]; a = {}; Do[ If[selDivs[n] == 0, AppendTo[a, n]; Print[n]], {n, 2, 10^6}]; a (* after Alonso del Arte at A194472 *)

Crossrefs

Cf. A188999, A194472, A222266, A286324.

Sequence in context: A269029 A004325 A075621 * A137499 A371068 A122813

Adjacent sequences: A293615 A293616 A293617 * A293619 A293620 A293621

Keyword

nonn,more

Author

Amiram Eldar, Oct 13 2017

Status

approved