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

Author

Amiram Eldar, May 27 2017

Keywords

• nonn

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

Crossrefs

Cf. A005153, A034448, A265501, A287173.

Programs

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]