A342398 Numbers k such that there is a subset of the nontrivial unitary divisors of k, {d|k : 1 < d < k, gcd(d, k/d) = 1}, that adds up to k.

30, 42, 66, 78, 102, 114, 138, 150, 174, 186, 210, 222, 246, 258, 282, 294, 318, 330, 354, 366, 390, 402, 420, 426, 438, 462, 474, 498, 510, 534, 546, 570, 582, 606, 618, 630, 642, 654, 660, 678, 690, 714, 726, 750, 762, 770, 780, 786, 798, 822, 834, 840, 858

Offset: 1

Author

Amiram Eldar, Mar 10 2021

Keywords

• nonn

Examples

			30 is a term since its proper unitary divisors, 1 < d < 30, are {2, 3, 5, 6, 10, 15}, and 5 + 10 + 15 = 30.
		

Links

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

Crossrefs

The unitary version of A136446.

Subsequence of A034683 and A293188.

Programs

Mathematica

q[n_] := Module[{d = Most @ Select[Divisors[n], CoprimeQ[#, n/#] &], x}, Plus @@ d >= n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, 2, Length[d]}], {x, 0, n}], n] > 0]; Select[Range[1000], q]