

A283550


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


3



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
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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: A285100 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



