A303357 - OEIS

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).

%I #8 Apr 26 2018 05:45:39

%S 295680,13278720,363095040,454755840,675333120,694256640,845053440,

%T 1038428160,2274455040,2357921280,3099048960,5021076480,6114339840,

%U 9643096320,9817328640,14495416320,17121377280,23787294720,30583418880,36277463040,45129477120,114499338240,211380879360

%N 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).

%C The unitary version of A181595.

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

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

%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; aQ[n_] :=

%t 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

%Y Cf. A034448, A181595, A303356.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 22 2018

%E a(9)-a(23) from _Giovanni Resta_, Apr 26 2018