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Search: id:A102715
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| A102715 |
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Triangle read by rows: T(n,k) is phi(binom(n,k)), where phi is Euler's totient function (0<=k<=n). |
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1
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| 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 4, 4, 4, 4, 1, 1, 2, 8, 8, 8, 2, 1, 1, 6, 12, 24, 24, 12, 6, 1, 1, 4, 12, 24, 24, 24, 12, 4, 1, 1, 6, 12, 24, 36, 36, 24, 12, 6, 1, 1, 4, 24, 32, 48, 72, 48, 32, 24, 4, 1, 1, 10, 40, 80, 80, 120, 120, 80, 80, 40, 10, 1, 1, 4, 20, 80, 240, 240
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Row n contains n+1 terms. Row sums yield A064450. T(2n,n)=A066973(n)
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FORMULA
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T(n, k)=phi(binom(n, k)) (0<=k<=n).
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EXAMPLE
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T(6,3)=8 because the positive integers relatively prime to binom(6,3)=20 and not exceeding 20 are 1,3,7,9,11,13,17 and 19.
Triangle begins:
1;
1,1;
1,1,1;
1,2,2,1;
1,2,2,2,1;
1,4,4,4,4,1;
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MAPLE
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with(numtheory): T:=(n, k)->phi(binomial(n, k)): for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A064450, A066973.
Sequence in context: A113971 A109338 A071202 this_sequence A047846 A025885 A087011
Adjacent sequences: A102712 A102713 A102714 this_sequence A102716 A102717 A102718
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 06 2005
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