A286652 Unitary practical numbers: numbers n such that every 1 <= k <= usigma(n) is a sum of distinct unitary divisors of n.

1, 2, 6, 30, 42, 66, 78, 210, 330, 390, 462, 510, 546, 570, 690, 714, 798, 858, 870, 930, 966, 1050, 1110, 1122, 1218, 1230, 1254, 1290, 1302, 1326, 1410, 1470, 1482, 1518, 1554, 1590, 1650, 1722, 1770, 1794, 1806, 1830, 1914, 1950, 1974, 2010, 2046, 2130

Offset

1,2

Comments

The unitary version of A005153. The squarefree terms of both sequences are the same, A265501. The nonsquarefree terms of this sequence are in A287173.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Mathematica

usigma[n_] :=  Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[#, n/#] == 1 &]]; uPracticalQ[n_] :=  Module[{f, p, e, prod = 1, ok = True}, If[n < 1 || (n > 1 && OddQ[n]), False, If[n == 1, True, f = FactorInteger[n]; {p, e} = Transpose[f]; r = Sort[p^e]; Do[If[r[[i]] > 1 + usigma[prod], ok = False; Break[]]; prod = prod*r[[i]], {i, Length[p]}]; ok]]]; Select[ Range[100000], uPracticalQ]

Crossrefs

Cf. A005153, A034448, A265501, A287173.

Sequence in context: A330326 A006954 A360681 * A265501 A090801 A166062

Adjacent sequences: A286649 A286650 A286651 * A286653 A286654 A286655

Keyword

nonn

Author

Amiram Eldar, May 27 2017

Status

approved