A377488 Irregular triangle r ead by rows where row n lists powers p^k for primes p | n such that k = floor(log n/log p).

1, 2, 3, 4, 5, 3, 4, 7, 8, 9, 5, 8, 11, 8, 9, 13, 7, 8, 5, 9, 16, 17, 9, 16, 19, 5, 16, 7, 9, 11, 16, 23, 9, 16, 25, 13, 16, 27, 7, 16, 29, 16, 25, 27, 31, 32, 11, 27, 17, 32, 7, 25, 27, 32, 37, 19, 32, 13, 27, 25, 32, 41, 7, 27, 32, 43, 11, 32, 25, 27, 23, 32

Offset: 1

Author

Michael De Vlieger, Nov 01 2024

Keywords

• nonn
• tabf
• easy

Comments

Row 1 is {1} by convention, since 1 is the empty product.

Examples

			Table of the first 12 rows:
   1:  1;
   2:  2;
   3:  3:
   4:  4;
   5:  5;
   6:  3, 4;
   7:  7;
   8:  8;
   9:  9;
  10:  5, 8;
  11: 11;
  12:  8, 9.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..11739 (rows n = 1..5000, flattened)
• Michael De Vlieger, Log log scatterplot of rows n of this sequence, n = 1.2^20 (2996045 terms).

Crossrefs

Cf. A001221, A064446, A339378, A377485.

Programs

Mathematica

{{1}}~Join~Table[Union[Join @@ Map[#^Range[Floor@ Log[#, n]] &, FactorInteger[n][[All, 1]] ] ], {n, 2, 30}]

Formula

Row n is { p^k : p | n, k = floor(log n/log p) }.

Row p^k = { p^k } for prime p and k > 0.

A001221(n) = length of row n for n > 1.

A064446(n) = product of row n.

A339378(n) = sum of row n for n > 1.