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 A334972 Bi-unitary admirable numbers: numbers k such that there is a proper bi-unitary divisor d of k such that bsigma(k) - 2*d = 2*k, where bsigma is the sum of bi-unitary divisors function (A188999). 5
 24, 30, 40, 42, 48, 54, 56, 66, 70, 78, 80, 88, 102, 104, 114, 120, 138, 150, 162, 174, 186, 222, 224, 246, 258, 270, 282, 294, 318, 354, 360, 366, 402, 420, 426, 438, 448, 474, 498, 534, 540, 582, 606, 618, 630, 642, 654, 660, 672, 678, 720, 726, 762, 780, 786 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, numbers that are equal to the sum of their proper bi-unitary divisors, with one of them taken with a minus sign. Admirable numbers (A111592) that are exponentially odd (A268335) are also bi-unitary admirable numbers since all of their divisors are bi-unitary. Terms that are not exponentially odd are 48, 80, 150, 162, 294, 360, 420, 448, 540, 630, 660, 720, 726, 780, 832, 990, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 48 is in the sequence since 48 = 1 + 2 + 3 - 6 + 8 + 16 + 24 is the sum of its proper bi-unitary divisors with one of them, 6, taken with a minus sign. MATHEMATICA fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); buDivQ[n_, 1] = True; buDivQ[n_, div_] := If[Mod[#2, #1] == 0, Last@Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; buAdmQ[n_] := (ab = bsigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && buDivQ[n, ab/2]; Select[Range, buAdmQ] CROSSREFS The bi-unitary version of A111592. Subsequence of A292982. Cf. A188999, A222266, A268335, A328328, A334974. Sequence in context: A068544 A284174 A292982 * A109797 A129656 A334974 Adjacent sequences:  A334969 A334970 A334971 * A334973 A334974 A334975 KEYWORD nonn AUTHOR Amiram Eldar, May 18 2020 STATUS approved

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Last modified April 17 16:59 EDT 2021. Contains 343063 sequences. (Running on oeis4.)