A081523 -id:A081523 - cp's OEIS frontend

A081524 a(n) = A081523(n)/n.

Original entry on oeis.org

1, 2, 4, 4, 4, 9, 5, 8, 8, 13, 7

Offset: 1

Amarnath Murthy, Mar 27 2003

Cf. A081521, A081522, A081523.

a(8)-a(11) from Jinyuan Wang, May 23 2020

A081521 Triangle read by rows: row n contains n terms in increasing order, relatively prime to n, whose sum is a multiple of n and such that the row contains the smallest possible subset of consecutive numbers starting with 1.

Original entry on oeis.org

1, 1, 3, 1, 4, 7, 1, 3, 5, 7, 1, 2, 3, 6, 8, 1, 5, 7, 11, 13, 17, 1, 2, 3, 4, 5, 8, 12, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 4, 5, 7, 8, 10, 13, 22, 1, 3, 7, 9, 11, 13, 17, 19, 21, 29, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 20

Offset: 1

Amarnath Murthy, Mar 27 2003

The "smallest set of n distinct numbers" is not a well-defined term in the definition. Why is row 5 "1,2,3,6,8" but not "1,2,4,6,7"? Why is row 7 "1,2,3,4,5,8,12" but not "1,2,4,5,6,8,9"? - R. J. Mathar, Nov 12 2006

			Triangle begins:
  1;
  1, 3;
  1, 4, 7;
  1, 3, 5,  7;
  1, 2, 3,  6,  8;
  1, 5, 7, 11, 13, 17;
  1, 2, 3,  4,  5,  8, 12;
  ...

Cf. A081522, A081523, A081524.

row(n) = {my(m=n*(n-1)/2, v); forstep(k=m+n/(2-n%2), oo, n, v=List([]); for(i=2, k-m, if(gcd(n, i)==1, listput(v, i))); if(#v>n-2, forsubset([#v, n-1], w, if(r=1+sum(i=1, n-1, v[w[i]])==k, return(concat(1, vector(n-1, i, v[w[i]]))))))); } \\ Jinyuan Wang, May 24 2020

New definition proposed by Omar E. Pol, Mar 24 2008, in an attempt to answer R. J. Mathar's questions.

Name corrected and more terms from Jinyuan Wang, May 24 2020

A081522 Last term in row n of A081521.

Original entry on oeis.org

1, 3, 7, 7, 8, 17, 12, 15, 22, 29, 20

Offset: 1

Amarnath Murthy, Mar 27 2003

Cf. A081521, A081523, A081524.

a(8)-a(11) from Jinyuan Wang, May 24 2020

cp's OEIS Frontend

A081524 a(n) = A081523(n)/n.

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A081521 Triangle read by rows: row n contains n terms in increasing order, relatively prime to n, whose sum is a multiple of n and such that the row contains the smallest possible subset of consecutive numbers starting with 1.

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A081522 Last term in row n of A081521.

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