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A364728
Numbers that are not the sum of admirable numbers (not necessarily distinct).
1
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
Analogous sequence with abundant numbers: A283550.
Sequence in context: A048991 A321292 A131881 * A053460 A304678 A316529
KEYWORD
nonn,fini,full
AUTHOR
Amiram Eldar, Aug 05 2023
STATUS
approved