cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

24, 360, 4320, 14688, 1468800, 9547200, 50585472, 54198720, 189695520, 1680459264
Offset: 1

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Author

Amiram Eldar, Sep 14 2019

Keywords

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.

Examples

			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.
		

Crossrefs

Programs

  • 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 *)

A327944 Numbers m that are equal to the sum of their first k consecutive nonunitary divisors, but not all of them (i.e k < A048105(m)).

Original entry on oeis.org

480, 2688, 17640, 131712, 2095104, 3576000, 4248288, 16854816, 41055200, 400162032, 637787520, 788259840, 1839272960, 2423592576
Offset: 1

Views

Author

Amiram Eldar, Sep 30 2019

Keywords

Comments

The nonunitary version of Erdős-Nicolas numbers (A194472).
If all the nonunitary divisors are permitted (i.e. k <= A048105(n)), then the nonunitary perfect numbers (A064591) are included.

Examples

			480 is in the sequence since its nonunitary divisors are 2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240 and 2 + 4 + 6 + 8 + 10 + 12 + 16 + 20 + 24 + 30 + 40 + 48 + 60 + 80 + 120 = 480.~
		

Crossrefs

Programs

  • Mathematica
    ndivs[n_] := Block[{d = Divisors[n]}, Select[d, GCD[ #, n/# ] > 1 &]]; ndivs2[n_] := Module[{d=ndivs[n]},If[Length[d]<2,{},Drop[d, -1] ]]; subtr = If[#1 < #2, Throw[#1], #1 - #2] &; selDivs[n_] := Catch@Fold[subtr, n,ndivs2[n]]; a = {}; Do[ If[selDivs[n] == 0, AppendTo[a, n]; Print[n]], {n, 2, 10^6}]; a (* after Alonso del Arte at A194472 *)
Showing 1-2 of 2 results.