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A034090
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Numbers k whose sum of proper divisors (A001065(k)) exceeds that of all smaller numbers.
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15
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1, 2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 216, 240, 288, 300, 336, 360, 420, 480, 504, 540, 600, 660, 720, 840, 960, 1008, 1080, 1200, 1260, 1440, 1560, 1680, 1980, 2100, 2160, 2340, 2400, 2520, 2880, 3120, 3240
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OFFSET
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1,2
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COMMENTS
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The highly abundant numbers A002093 are a subsequence since if sigma(k) - k > sigma(m) - m for all m < n then sigma(k) > sigma(m). - Charles R Greathouse IV, Sep 13 2016
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LINKS
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EXAMPLE
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-- 12: 1+2+3+4+6 = 16
13: 1 = 1
14: 1+2+7 = 10
15: 1+3+5 = 9
16: 1+2+4+8 = 15
17: 1 = 1
-- 18: 1+2+3+6+9 = 21
As 12 had the previous (earliest) highest, it is a term; then since 18 has the new highest, it is a term. (End)
Table of initial values of n, a(n), A034091(n) = f(a(n)), where f(k) = sigma(k)-k = A001065(k):
1, 1, 0
2, 2, 1
3, 4, 3
4, 6, 6
5, 8, 7
6, 10, 8
7, 12, 16
8, 18, 21
9, 20, 22
10, 24, 36
11, 30, 42
12, 36, 55
13, 48, 76
14, 60, 108
15, 72, 123
16, 84, 140
17, 90, 144
18, 96, 156
19, 108, 172
20, 120, 240
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MATHEMATICA
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A = {}; mx = -1; For[ k = 1, k < 10000, k++, t = DivisorSigma[1, k] - k; If[ t > mx, mx = t; AppendTo[A, k]]]; A (* slightly modified by Robert G. Wilson v, Aug 28 2022 *)
DeleteDuplicates[Table[{n, DivisorSigma[1, n]-n}, {n, 5000}], GreaterEqual[ #1[[2]], #2[[2]]]&][[All, 1]] (* Harvey P. Dale, Jan 15 2023 *)
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PROG
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CROSSREFS
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This sequence and A034091 together give the record high points in A001065.
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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