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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). 1
 24, 360, 4320, 14688, 1468800, 9547200, 50585472, 54198720, 189695520, 1680459264 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)