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

Author

Amiram Eldar, Mar 10 2017

Keywords

• nonn
• fini
• full

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.

Examples

			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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..496
• Giovanni Resta, abundant numbers

Crossrefs

Cf. A271113, A048242, A005101.

Programs

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]]