A334217 Irregular table T(n, k) read by rows, n > 0 and k = 1..A334216(n); n-th row corresponds to distinct terms of n-th row of A334215, in ascending order.

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 6, 1, 7, 1, 2, 8, 1, 3, 9, 1, 10, 1, 11, 1, 2, 12, 1, 13, 1, 14, 1, 15, 1, 2, 4, 16, 1, 17, 1, 3, 18, 1, 19, 1, 2, 20, 1, 21, 1, 22, 1, 23, 1, 2, 24, 1, 5, 25, 1, 26, 1, 3, 27, 1, 2, 28, 1, 29, 1, 30, 1, 31, 1, 2, 4, 32, 1, 33

Offset: 1

Author

Rémy Sigrist, Apr 19 2020

Keywords

• nonn
• tabf

Examples

			The first rows are:
  n     n-th row
  --    -------------
   1    [1]
   2    [1, 2]
   3    [1, 3]
   4    [1, 2, 4]
   5    [1, 5]
   6    [1, 6]
   7    [1, 7]
   8    [1, 2, 8]
   9    [1, 3, 9]
  10    [1, 10]
  11    [1, 11]
  12    [1, 2, 12]
  13    [1, 13]
  14    [1, 14]
  15    [1, 15]
  16    [1, 2, 4, 16]
		

Crossrefs

Cf. A000188, A261969, A334215, A334216.

Programs

PARI

row(n) = { my (f=factor(n)); Set(apply (k -> prod (i=1, #f~, f[i,1]^(f[i,2]\k)), [1..1+if (n==1, 0, vecmax(f[,2]~))])) }

Formula

T(n, 1) = 1.

T(n, 2) = A261969(n) for any n > 1.

T(n, A334216(n)-1) = A000188(n) for any n > 1.

T(n, A334216(n)) = n.