A303357 Unitary near-perfect numbers: unitary abundant numbers n such that usigma(n) - 2n is a unitary divisor of n, where usigma(n) is the sum of unitary divisors of n (A034448).

295680, 13278720, 363095040, 454755840, 675333120, 694256640, 845053440, 1038428160, 2274455040, 2357921280, 3099048960, 5021076480, 6114339840, 9643096320, 9817328640, 14495416320, 17121377280, 23787294720, 30583418880, 36277463040, 45129477120, 114499338240, 211380879360

Offset

1,1

Comments

The unitary version of A181595.

All the terms up to a(23) are divisible by 2^8 * 3 * 5. - Giovanni Resta, Apr 26 2018

Links

Table of n, a(n) for n=1..23.

Example

295680 is in the sequence since usigma(295680) - 2*295680 = 592128 - 591360 = 768 and 768 is a unitary divisor of 295680.

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; aQ[n_] :=
Module[{d}, d = usigma[n] - 2 n; If[d <= 0, False, Divisible[n, d] && GCD[d, n/d] == 1]]; n = 1; seq={}; Do[ If[aQ[n], AppendTo[seq, n]]; n++, {k, 1, 300000}]; seq

Crossrefs

Cf. A034448, A181595, A303356.

Sequence in context: A109031 A137817 A137818 * A251387 A164946 A204318

Adjacent sequences: A303354 A303355 A303356 * A303358 A303359 A303360

Keyword

nonn

Author

Amiram Eldar, Apr 22 2018

Extensions

a(9)-a(23) from Giovanni Resta, Apr 26 2018

Status

approved