%I #8 Aug 05 2023 13:17:01

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,28,29,

%T 31,33,34,35,37,38,39,41,43,45,46,47,48,49,51,53,55,57,58,59,61,63,65,

%U 67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101

%N Numbers that are not the sum of admirable numbers (not necessarily distinct).

%C First differs from A053460 at n = 39.

%C _Giovanni Resta_ found that 1003 is the largest number that is not a sum of admirable numbers.

%H Amiram Eldar, <a href="/A364728/b364728.txt">Table of n, a(n) for n = 1..504</a> (complete sequence)

%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/admirable_number">admirable numbers</a>, Numbers Aplenty.

%t admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];

%t With[{adm = Select[Range[1200], admQ]}, Position[Rest[CoefficientList[Series[Product[(1 + x^adm[[k]]), {k, 1, Length[adm]}], {x, 0, adm[[-1]]}], x]], 0] // Flatten]

%Y Cf. A053460, A111592.

%Y Analogous sequence with abundant numbers: A283550.

%K nonn,fini,full

%O 1,2

%A _Amiram Eldar_, Aug 05 2023