A266531 Square array read by antidiagonals upwards: T(n,k) = n-th number with k odd divisors.

1, 2, 3, 4, 5, 9, 8, 6, 18, 15, 16, 7, 25, 21, 81, 32, 10, 36, 27, 162, 45, 64, 11, 49, 30, 324, 63, 729, 128, 12, 50, 33, 625, 75, 1458, 105, 256, 13, 72, 35, 648, 90, 2916, 135, 225, 512, 14, 98, 39, 1250, 99, 5832, 165, 441, 405, 1024, 17, 100, 42, 1296, 117, 11664, 189, 450, 567, 59049, 2048, 19, 121, 51, 2401, 126, 15625

Offset

1,2

Comments

T(n,k) is the n-th positive integer with exactly k odd divisors.

This is a permutation of the natural numbers.

T(n,k) is also the n-th number j with the property that the symmetric representation of sigma(j) has k subparts (cf. A279387). - Omar E. Pol, Dec 27 2016

T(n,k) is also the n-th positive integer with exactly k partitions into consecutive parts. - Omar E. Pol, Aug 16 2018

Links

Table of n, a(n) for n=1..73.

Index entries for sequences that are permutations of the natural numbers

Example

The corner of the square array begins:
    1,  3,  9, 15,   81,  45,   729, 105,  225,  405, ...
    2,  5, 18, 21,  162,  63,  1458, 135,  441,  567, ...
    4,  6, 25, 27,  324,  75,  2916, 165,  450,  810, ...
    8,  7, 36, 30,  625,  90,  5832, 189,  882,  891, ...
   16, 10, 49, 33,  648,  99, 11664, 195,  900, 1053, ...
   32, 11, 50, 35, 1250, 117, 15625, 210, 1089, 1134, ...
   64, 12, 72, 39, 1296, 126, 23328, 231, 1225, 1377, ...
  128, 13, 98, 42, 2401, 147, 31250, 255, 1521, 1539, ...
  ...

Crossrefs

Row 1 is A038547.

Column 1-10: A000079, A038550, A072502, apparently A131651, A267696, A230577, A267697, A267891, A267892, A267893.

Cf. A001227, A182469, A236104, A237591, A237593, A240062, A261697, A261698, A261699, A279387, A286000, A286001, A296508.

Sequence in context: A335910 A362814 A371152 * A284311 A357581 A174225

Adjacent sequences: A266528 A266529 A266530 * A266532 A266533 A266534

Keyword

nonn,tabl

Author

Omar E. Pol, Apr 02 2016

Status

approved