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A129246
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Iterated sum of divisors array A[k,n] = k-th iterate of sigma(n), by antidiagonals.
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5
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1, 1, 3, 1, 4, 4, 1, 7, 7, 7, 1, 8, 8, 8, 6, 1, 15, 15, 15, 12, 12, 1, 24, 24, 24, 28, 28, 8, 1, 60, 60, 60, 56, 56, 15, 15, 1, 168, 168, 168, 120, 120, 24, 24, 13, 1, 480, 480, 480, 360, 360, 60, 60, 14, 18, 1, 1512, 1512, 1512, 1170, 1170, 168, 168, 24, 39, 12, 1, 4800, 4800
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| First row is sigma(n) = sum of divisors of n = A000203. Second row is sigma(sigma(n)) = A051027. Third Row is sigma(sigma(sigma(n))) = A066971. 4th row is sigma(sigma(sigma(sigma(n)))). Main diagonal is A[n,n] = A000203(A000203(A000203(...A000203(n)...))) where iteration is n deep = A090896(n). First column is all 1. Second column is A007497.
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FORMULA
| A[k,n] = sigma^k(n), where sigma^k denotes functional iteration.
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EXAMPLE
| Array begins:
k / sigma(...sigma(n)..) nested k deep.
1.|.1...3...4....7....6....12....8....15...13....18...
2.|.1...4...7....8...12....28...15....24...14....39...
3.|.1...7...8...15...28....56...24....60...24....56...
4.|.1...8..15...24...56...120...60...168...60...120...
5.|.1..15..24...60..120...360..168...480..168...360...
6.|.1..24..60..168..360..1170..480..1512..480..1170...
7.|.1..60.168..480.1170..3276.1512..4800.1512..3276...
8.|.1.168.480.1512.3276.10192.4800.15748.4800.10192...
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MAPLE
| A129246 := proc(k, n) option remember ; if k= 1 then numtheory[sigma](n); else A129246(k-1, numtheory[sigma](n)) ; fi ; end: for d from 1 to 13 do for n from 1 to d do printf("%d, ", A129246(d+1-n, n)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
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CROSSREFS
| Cf. A000203, A007497, A051027, A066971, A090896.
Sequence in context: A060043 A054907 A089554 * A125608 A099813 A141300
Adjacent sequences: A129243 A129244 A129245 * A129247 A129248 A129249
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 27 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
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