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

1,1

Links

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

Example

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

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]

Crossrefs

The unitary version of A136446.

Subsequence of A034683 and A293188.

Sequence in context: A306330 A160352 A291446 * A226104 A091455 A367481

Adjacent sequences: A342395 A342396 A342397 * A342399 A342400 A342401

Keyword

nonn

Author

Amiram Eldar, Mar 10 2021

Status

approved