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A127368
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Relative prime triangle, read by rows.
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7
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1, 1, 0, 1, 2, 0, 1, 0, 3, 0, 1, 2, 3, 4, 0, 1, 0, 0, 0, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 0, 3, 0, 0, 0, 7, 0, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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Row sums = A023896, (reduced residue system mod n): (1, 1, 3, 4, 10, 6, 21,...). [From Gary W. Adamson, Aug 27 2008]
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LINKS
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Table of n, a(n) for n=1..91.
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FORMULA
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T(n,k) = k if a relative prime of n; 0 otherwise. Replace the "1's" of A054521 with their corresponding column numbers; leaving the zeros.
Equals A054521 * A127648 as infinite lower triangular matrices. [From Gary W. Adamson, Aug 27 2008]
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EXAMPLE
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Row 4 = (1, 0, 3, 0) since 1 and 3 are relative primes of 4.
First few rows of the triangle are:
1;
1, 0;
1, 2, 0;
1, 0, 3, 0;
1, 2, 3, 4, 0;
1, 0, 0, 0, 5, 0;
1, 2, 3, 4, 5, 6, 0;
...
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PROG
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(PARI) [Contribution from M. F. Hasler, Mar 02 2012] (Start)
T127368(n, k)={gcd(n, k)==1 & return(k)}
A127368(n)=T127368( t=(sqrt(8*n)+1)\2, n-binomial(t, 2)) \\ (End)
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CROSSREFS
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Cf. A054521.
A054521, A023896 [From Gary W. Adamson, Aug 27 2008]
Sequence in context: A175267 A108045 A143728 * A112552 A048154 A134511
Adjacent sequences: A127365 A127366 A127367 * A127369 A127370 A127371
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Jan 11 2007
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EXTENSIONS
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Corrected at the suggestion of Kevin Ryde by Alois P. Heinz, Mar 02 2012
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STATUS
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approved
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