A309843 Numbers m that equal the sum of their first k consecutive aliquot infinitary divisors, but not all of them (i.e k < A037445(m) - 1).

24, 360, 4320, 14688, 1468800, 9547200, 50585472, 54198720, 189695520, 1680459264

Offset

1,1

Comments

The infinitary version of Erdős-Nicolas numbers (A194472).

If all the aliquot infinitary divisors are permitted (i.e. k <= A037445(n) - 1), then the infinitary perfect numbers (A007357) are included.

Links

Table of n, a(n) for n=1..10.

Example

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

Mathematica

idivs[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[ x ] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n, Drop[idivs[n], -2]]; s= {}; Do[If[selDivs[n] == 0, AppendTo[s, n]], {n, 2, 10^6}]; s(* after Alonso del Arte at A194472 *)

Crossrefs

Cf. A007357, A077609, A037445, A049417, A194472, A293618.

Sequence in context: A122813 A028245 A005546 * A081144 A126780 A052741

Adjacent sequences: A309840 A309841 A309842 * A309844 A309845 A309846

Keyword

nonn,more

Author

Amiram Eldar, Sep 14 2019

Status

approved