A334898 Bi-unitary practical numbers: numbers m such that every number 1 <= k <= bsigma(m) is a sum of distinct bi-unitary divisors of m, where bsigma is A188999.

1, 2, 6, 8, 24, 30, 32, 40, 42, 48, 54, 56, 66, 72, 78, 88, 96, 104, 120, 128, 160, 168, 192, 210, 216, 224, 240, 264, 270, 280, 288, 312, 320, 330, 336, 352, 360, 378, 384, 390, 408, 416, 432, 440, 448, 456, 462, 480, 486, 504, 510, 512, 520, 528, 544, 546, 552

Offset

1,2

Comments

Includes 1 and all the odd powers of 2 (A004171). The other terms are a subset of bi-unitary abundant numbers (A292982) and bi-unitary pseudoperfect numbers (A292985).

Links

Amiram Eldar, Table of n, a(n) for n = 1..2500

Mathematica

biunitaryDivisorQ[div_, n_] := If[Mod[#2, #1] == 0, Last @ Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; bdivs[n_] := Module[{d = Divisors[n]}, Select[d, biunitaryDivisorQ[#, n] &]]; bPracQ[n_] := Module[{d = bdivs[n], sd, x}, sd = Plus @@ d; Min @ CoefficientList[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, sd}], x] >  0]; Select[Range[1000], bPracQ]

Crossrefs

The bi-unitary version of A005153.

Cf. A004171, A188999, A286652, A292982, A292985, A334901.

Sequence in context: A344914 A068496 A340810 * A081957 A334901 A279732

Adjacent sequences: A334895 A334896 A334897 * A334899 A334900 A334901

Keyword

nonn

Author

Amiram Eldar, May 16 2020

Status

approved