A079786 Triangle read by rows in which the n-th row begins with n and contains at most tau(n) numbers. The r-th term from right is the largest number < n with r divisors, for 1 <= r <= tau(n) skipping any r for which no suitable number exists.

1, 2, 1, 3, 1, 4, 3, 1, 5, 1, 6, 4, 5, 1, 7, 1, 8, 4, 7, 1, 9, 7, 1, 10, 9, 7, 1, 11, 1, 12, 10, 9, 11, 1, 13, 1, 14, 9, 13, 1, 15, 9, 13, 1, 16, 15, 9, 13, 1, 17, 1, 18, 16, 15, 9, 17, 1, 19, 1, 20, 16, 15, 9, 19, 1, 21, 9, 19, 1, 22, 9, 19, 1, 23, 1, 24, 20, 16, 22, 9, 23, 1, 25, 23, 1, 26, 25

Offset

1,2

Comments

The number of terms in the n-th row <= tau(n).

Links

Alois P. Heinz, Rows n = 1..2700

Example

Triangle begins:
   1;
   2,  1;
   3,  1;
   4,  3, 1;
   5,  1;
   6,  4, 5,  1;
   7,  1;
   8,  4, 7,  1;
   9,  7, 1,
  10,  9, 7,  1;
  11,  1;
  12, 10, 9, 11, 1;
  ...
Row 12 has only 5 terms and tau(12) = 6.

Prog

(PARI) print(1, ", "); for(i=2, 50, v=[1]; for(j=2, sigma(i, 0), forstep(k=i, 1, -1, if(sigma(k, 0)==j, v=concat(v, k); break))); forstep(l=length(v), 1, -1, print1(v[l], ", ")); print()) \\ Lambert Herrgesell (zero815(AT)googlemail.com), Mar 13 2006

Crossrefs

Cf. A000005, A079787.

Sequence in context: A354185 A322994 A256147 * A032451 A214494 A088445

Adjacent sequences: A079783 A079784 A079785 * A079787 A079788 A079789

Keyword

nonn,look,tabf

Author

Amarnath Murthy, Feb 03 2003

Extensions

More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Mar 13 2006

Offset corrected by Andrew Howroyd, Sep 29 2024

Name clarified by Sean A. Irvine, Aug 26 2025

Status

approved