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

Author

Rémy Sigrist, May 30 2018

Keywords

• nonn
• tabf

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.

Examples

			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]
		

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

Crossrefs

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

Programs

PARI

See Links section.

Formula

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

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