A328446 Table read by rows: the n-th row gives the nonnegative integers k such that n - k is a power of k.

0, 1, 2, 2, 3, 4, 2, 3, 5, 6, 4, 7, 8, 2, 5, 9, 10, 3, 6, 11, 12, 7, 13, 14, 8, 15, 16, 2, 9, 17, 18, 4, 10, 19, 20, 11, 21, 22, 12, 23, 24, 13, 25, 26, 14, 27, 28, 3, 5, 15, 29, 30, 16, 31, 32, 2, 17, 33, 34, 18, 35, 36, 19, 37, 38, 20, 39, 40, 6, 21, 41, 42, 22

Offset

1,3

Comments

The n-th row has length A309978(n) for n > 1.

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Example

Table begins
   n | n-th row
  ---+----------
   1 | 0
   2 | 1
   3 | 2
   4 | 2, 3
   5 | 4
   6 | 2, 3, 5
   7 | 6
   8 | 4, 7
   9 | 8
  10 | 2, 5, 9
  11 | 10
  12 | 3, 6, 11
  13 | 12
  14 | 7, 13
  15 | 14
  16 | 8, 15
  17 | 16
  18 | 2, 9, 17
For n = 10 the 10th row is 2, 5, 9 because
10 - 2 = 2^3,
10 - 5 = 5^1, and
10 - 9 = 9^0.

Prog

(PARI) row(n) = {if (n==1, return ([0])); my(row = vector(0)); fordiv(n, d, if ((d>1) && (d<n) && (d^valuation(n-d, d) == n-d), row = concat(row, d))); concat(row, n-1); }
tabf(nn) = {for (n=1, nn, print(row(n)); ); } \\ Michel Marcus, Oct 16 2019

Crossrefs

Cf. A307092, A309978.

Sequence in context: A159978 A230546 A286617 * A371306 A257062 A098223

Adjacent sequences: A328443 A328444 A328445 * A328447 A328448 A328449

Keyword

nonn,tabf

Author

Peter Kagey, Oct 15 2019

Status

approved