A328328 Unitary admirable numbers: numbers k such that there is a proper unitary divisor d of k such that usigma(k) - 2d = 2k, where usigma is the sum of unitary divisors function (A034448).

30, 42, 66, 70, 78, 102, 114, 138, 150, 174, 186, 222, 246, 258, 282, 294, 318, 354, 366, 402, 420, 426, 438, 474, 498, 534, 582, 606, 618, 630, 642, 654, 660, 678, 726, 750, 762, 780, 786, 822, 834, 840, 894, 906, 942, 978, 990, 1002, 1014, 1020, 1038, 1074, 1086

Offset

1,1

Comments

Differs from A302574(n) at n >= 30.

Equivalently, numbers that equal to the sum of their proper unitary divisors, with one of them taken with a minus sign.

The unitary version of A111592.

The squarefree terms are also admirable numbers (A111592). The nonsquarefree terms are 150, 294, 420, 630, 660, 726, 750, 780, 840, 990, ...

The unitary abundant numbers (A034683) that are not unitary admirable numbers are: 210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 924, 930, 966, ...

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

150 is in the sequence since 150 = 1 + 2 + 3 - 6 + 25 + 50 + 75 is the sum of its proper unitary divisors with one of them, 6, taken with a minus sign.

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); aQ[n_] := (ab = usigma[n] - 2n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && CoprimeQ[2*n/ab, ab/2]; Select[Range[1086], aQ]

Crossrefs

Cf. A034448, A077610, A111592, A302574.

Subsequence of A034683 and A290466.

Sequence in context: A075819 A306217 A034683 * A302574 A087248 A249242

Adjacent sequences: A328325 A328326 A328327 * A328329 A328330 A328331

Keyword

nonn

Author

Amiram Eldar, Oct 12 2019

Status

approved