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

1,2

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.

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]

Crossrefs

Cf. A053460, A111592.

Analogous sequence with abundant numbers: A283550.

Sequence in context: A048991 A321292 A131881 * A053460 A304678 A316529

Adjacent sequences: A364725 A364726 A364727 * A364729 A364730 A364731

Keyword

nonn,fini,full

Author

Amiram Eldar, Aug 05 2023

Status

approved