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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)