A292985 - OEIS

%I #19 Mar 25 2023 05:27:13

%S 6,24,30,40,42,48,54,56,60,66,72,78,80,88,90,96,102,104,114,120,138,

%T 150,160,162,168,174,186,192,210,216,222,224,240,246,258,264,270,280,

%U 282,288,294,312,318,320,330,336,352,354,360,366,378,384,390,402,408

%N Bi-unitary pseudoperfect numbers: numbers that are equal to the sum of a subset of their aliquot bi-unitary divisors.

%C Analogous to pseudoperfect numbers (A005835) with bi-unitary sigma (A188999) instead of sigma (A000203).

%H Amiram Eldar, <a href="/A292985/b292985.txt">Table of n, a(n) for n = 1..10000</a>

%e 48 is in the sequence since its bi-unitary divisors are 1, 2, 3, 6, 8, 16, 24, 48 and 48 = 8 + 16 + 24.

%t f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; a = {}; n = 0; While[n < 1000, n++; d = Most[bdiv[n]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c > 0, AppendTo[a, n]]];a (* after _T. D. Noe_ at A005835 and _Michael De Vlieger_ at A188999 *)

%Y Cf. A005835, A188999.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 27 2017