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Search: id:A112592
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| A112592 |
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Triangle where a(1,1) = 0, a(n,m) = number of terms of row (n-1) which are coprime to m. |
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+0
3
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| 0, 1, 0, 2, 1, 1, 3, 2, 3, 2, 4, 2, 2, 2, 4, 5, 0, 5, 0, 5, 0, 6, 3, 3, 3, 0, 3, 3, 7, 5, 0, 5, 6, 0, 6, 5, 8, 4, 4, 4, 3, 4, 5, 4, 4, 9, 2, 8, 2, 8, 1, 9, 2, 8, 1, 10, 4, 8, 4, 10, 2, 10, 4, 8, 4, 10, 11, 0, 11, 0, 7, 0, 11, 0, 11, 0, 11, 0, 12, 6, 6, 6, 6, 6, 5, 6, 6, 6, 1, 6, 6, 13, 2, 2, 2, 12, 2, 13, 2
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.
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LINKS
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Diana Mecum, Table of n, a(n) for n = 1..2000 [From Diana Mecum (diana.mecum(AT)gmail.com), Aug 12 2008]
Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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Row 6 of the triangle is [5,0,5,0,5,0]. Among these terms there are 6 terms coprime to 1, 3 terms coprime to 2, 3 terms coprime to 3, 3 terms coprime to 4, 0 terms coprime to 5, 3 terms coprime to 6 and 3 terms coprime to 7. So row 7 is [6,3,3,3,0,3,3].
0,
1,0,
2,1,1,
3,2,3,2,
4,2,2,2,4,
5,0,5,0,5,0,
6,3,3,3,0,3,3,
7,5,0,5,6,0,6,5,
8,4,4,4,3,4,5,4,4
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MATHEMATICA
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f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length@p; t = Table[Count[GCD[p, n], 1], {n, k + 1}]; Return@Append[l, t]; ]; Nest[f, {{0}}, 13] // Flatten (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A112599.
Row sums are in A114719. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 01 2009]
Sequence in context: A117506 A055089 A060117 this_sequence A070036 A059779 A049346
Adjacent sequences: A112589 A112590 A112591 this_sequence A112593 A112594 A112595
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KEYWORD
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nonn,tabl
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AUTHOR
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Leroy Quet, Dec 24 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 27 2005
Terms a(100) through a(2000) from Diana Mecum (diana.mecum(AT)gmail.com), Aug 12 2008
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