A305325 Irregular triangle read by rows T(n, k), n >= 1 and 1 <= k <= A305215(n): T(n, k) is the k-th positive number with largest prime power factor equal to A000961(n).

1, 2, 3, 6, 4, 12, 5, 10, 15, 20, 30, 60, 7, 14, 21, 28, 35, 42, 70, 84, 105, 140, 210, 420, 8, 24, 40, 56, 120, 168, 280, 840, 9, 18, 36, 45, 63, 72, 90, 126, 180, 252, 315, 360, 504, 630, 1260, 2520, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 132, 154, 165

Offset

1,2

Comments

The largest prime power factor of a number n is given by A034699(n).

When interpreted as a flat sequence we obtain a permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..15360

Rémy Sigrist, PARI program for A305325

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, 1) = A000961(n).

T(n, A305215(n)) = A051451(n).

Example

Triangle begins:
  1: [1]
  2: [2]
  3: [3, 6]
  4: [4, 12]
  5: [5, 10, 15, 20, 30, 60]
  6: [7, 14, 21, 28, 35, 42, 70, 84, 105, 140, 210, 420]
  7: [8, 24, 40, 56, 120, 168, 280, 840]
  8: [9, 18, 36, 45, 63, 72, 90, 126, 180, 252, 315, 360, 504, 630, 1260, 2520]

Prog

(PARI) See Links section.

Crossrefs

Cf. A000961, A034699, A051451, A305215, A336816 (inverse).

Sequence in context: A104663 A358299 A246429 * A302848 A046202 A225642

Adjacent sequences: A305322 A305323 A305324 * A305326 A305327 A305328

Keyword

nonn,tabf

Author

Rémy Sigrist, May 30 2018

Status

approved