A364728 Numbers that are not the sum of admirable numbers (not necessarily distinct).

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, 31, 33, 34, 35, 37, 38, 39, 41, 43, 45, 46, 47, 48, 49, 51, 53, 55, 57, 58, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101

Offset: 1

Author

Amiram Eldar, Aug 05 2023

Keywords

• nonn
• fini
• full

Comments

First differs from A053460 at n = 39.

Giovanni Resta found that 1003 is the largest number that is not a sum of admirable numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..504 (complete sequence)
• Giovanni Resta, admirable numbers, Numbers Aplenty.

Crossrefs

Cf. A053460, A111592.

Analogous sequence with abundant numbers: A283550.

Programs

Mathematica

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