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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 10 2021
STATUS
approved

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)