A283550 Numbers that are not the sum of abundant numbers (not necessarily distinct).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 41, 43, 45, 46, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107

Offset

1,2

Comments

a(496) = 991 is the last term.

Subsequence of A048242 (Numbers that are not the sum of two abundant numbers).

Giovanni Resta noticed that 991 is the largest number that is not a sum of abundant numbers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..496

Giovanni Resta, abundant numbers

Example

20161 = 12 + 304 + 19845 is the sum of 3 abundant numbers and thus not in the sequence (although it is in A048242, since it is not the sum of 2 abundant numbers).

Mathematica

AbundantQ[n_] := DivisorSigma[1, n] > 2 n; a = Select[Range[1000], AbundantQ[#] &]; nn = Dimensions[a][[1]]; t = Rest[CoefficientList[ Series[Product[(1 + x^a[[k]]), {k, nn}], {x, 0, a[[-1]]}], x]]; f = Flatten[Position[t, 0]]

Crossrefs

Cf. A271113, A048242, A005101.

Sequence in context: A360553 A067340 A263837 * A271113 A325369 A317101

Adjacent sequences: A283547 A283548 A283549 * A283551 A283552 A283553

Keyword

nonn,fini,full

Author

Amiram Eldar, Mar 10 2017

Status

approved