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A127368 Relative prime triangle, read by rows. 7
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)
OFFSET

1,5

COMMENTS

Row sums = A023896, (reduced residue system mod n): (1, 1, 3, 4, 10, 6, 21,...). [From Gary W. Adamson, Aug 27 2008]

LINKS

Table of n, a(n) for n=1..91.

FORMULA

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]

EXAMPLE

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;

...

PROG

(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)

CROSSREFS

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

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 11 2007

EXTENSIONS

Corrected at the suggestion of Kevin Ryde by Alois P. Heinz, Mar 02 2012

STATUS

approved

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Last modified September 26 10:38 EDT 2017. Contains 292518 sequences.