A266531 - OEIS

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

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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, ...