A380600 Irregular table T(n, k), n > 0, k = 1..A000005(n) read by rows: the n-th row lists the numbers of the form n * (d-1) / d with d a positive divisor of n.

0, 0, 1, 0, 2, 0, 2, 3, 0, 4, 0, 3, 4, 5, 0, 6, 0, 4, 6, 7, 0, 6, 8, 0, 5, 8, 9, 0, 10, 0, 6, 8, 9, 10, 11, 0, 12, 0, 7, 12, 13, 0, 10, 12, 14, 0, 8, 12, 14, 15, 0, 16, 0, 9, 12, 15, 16, 17, 0, 18, 0, 10, 15, 16, 18, 19, 0, 14, 18, 20, 0, 11, 20, 21, 0, 22

Offset

1,5

Links

Table of n, a(n) for n=1..76.

Index entries for sequences related to divisors

Formula

T(n, k) = n * (A027750(n, k) - 1) / A027750(n, k).

Sum_{k = 1..A000005(n)} T(n, k) = A094471(n).

Product_{k = 2..A000005(n)} T(n, k) = A072513(n).

LCM{k = 2..A000005(n)} T(n, k) = A258324(n).

T(n, 1) = 0.

T(n, 2) = A060681(n) for any n > 1. - Michel Marcus, Feb 03 2025

T(n, A000005(n)-1) = A046666(n) for any n > 1.

T(n, A000005(n)) = n-1.

Example

Table T(n, k) begins:
  n   n-th row
  --  ------------------
   1  0
   2  0, 1
   3  0, 2
   4  0, 2, 3
   5  0, 4
   6  0, 3, 4, 5
   7  0, 6
   8  0, 4, 6, 7
   9  0, 6, 8
  10  0, 5, 8, 9
  11  0, 10
  12  0, 6, 8, 9, 10, 11
  13  0, 12
  14  0, 7, 12, 13

Mathematica

Table[Map[n*(# - 1)/# &, Divisors[n]], {n, 23}] // Flatten (* Michael De Vlieger, Feb 03 2025 *)

Prog

(PARI) row(n) = apply (d -> n*(d-1)/d, divisors(n))

Crossrefs

Cf. A000005, A027750, A046666, A060681, A072513, A094471 (row sums), A258324.

Sequence in context: A087509 A274097 A265400 * A181871 A269591 A262878

Adjacent sequences: A380597 A380598 A380599 * A380601 A380602 A380603

Keyword

nonn,tabf,easy

Author

Rémy Sigrist, Feb 02 2025

Status

approved