A328719 Triangular array read by rows: row n consists of the numbers k from 1 to n sorted in ascending lexicographic order of their sequences of p-adic valuations.

1, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 5, 3, 2, 4, 1, 5, 3, 2, 6, 4, 1, 7, 5, 3, 2, 6, 4, 1, 7, 5, 3, 2, 6, 4, 8, 1, 7, 5, 3, 9, 2, 6, 4, 8, 1, 7, 5, 3, 9, 2, 10, 6, 4, 8, 1, 11, 7, 5, 3, 9, 2, 10, 6, 4, 8, 1, 11, 7, 5, 3, 9, 2, 10, 6, 4, 12, 8, 1, 13, 11, 7, 5, 3, 9, 2, 10, 6, 4, 12, 8, 1, 13, 11, 7, 5, 3, 9, 2, 14, 10, 6, 4, 12, 8

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Example

12 = 2^2 * 3 can be viewed as a sequence (2, 1, 0, 0, ...) of p-adic valuations, and 20 = 2^2 * 5 as (2, 0, 1, 0, ...); (2, 0, 1, 0, ...) comes before (2, 1, 0, 0, ...) in lexicographic order, so 20 "<" 12 from that perspective.
The triangle begins:
  1,
  1,  2,
  1,  3,  2,
  1,  3,  2,  4,
  1,  5,  3,  2,  4,
  1,  5,  3,  2,  6,  4,
  1,  7,  5,  3,  2,  6,  4,
  1,  7,  5,  3,  2,  6,  4,  8,
  1,  7,  5,  3,  9,  2,  6,  4,  8,
  1,  7,  5,  3,  9,  2, 10,  6,  4,  8,
  1, 11,  7,  5,  3,  9,  2, 10,  6,  4,  8,
  1, 11,  7,  5,  3,  9,  2, 10,  6,  4, 12,  8,
  1, 13, 11,  7,  5,  3,  9,  2, 10,  6,  4, 12,  8,
  1, 13, 11,  7,  5,  3,  9,  2, 14, 10,  6,  4, 12,  8,
  1, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6,  4, 12,  8,
  1, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6,  4, 12,  8, 16,
  1, 17, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6,  4, 12,  8, 16,
  1, 17, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6, 18,  4, 12,  8, 16,
  1, 19, 17, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6, 18,  4, 12,  8, 16,
  1, 19, 17, 13, 11,  7,  5,  3, 15,  9,  2, 14, 10,  6, 18,  4, 20, 12,  8, 16,

Prog

(PARI) L=List(); n=1; while(n<=20, i=1; while(i<n&&factor(L[i]/n)[1, 2]<0, i++); listinsert(L, n, i); for(i=1, n, print1(L[i], ", ")); n++)

Crossrefs

Cf. A328720.

Sequence in context: A307081 A256440 A088370 * A113787 A115624 A076291

Adjacent sequences: A328716 A328717 A328718 * A328720 A328721 A328722

Keyword

nonn,tabl

Author

Luc Rousseau, Oct 26 2019

Status

approved