S000894


Pairs (m,k) with increasing m such that m is the first number having k divisors < sqrt(m).

2, 1, 6, 2, 12, 3, 24, 4, 48, 5, 60, 6, 120, 8, 144, 7, 180, 9, 240, 10, 360, 12, 720, 15, 840, 16, 900, 13, 960, 14, 1260, 18, 1680, 20, 2520, 24, 2880, 21, 3072, 11, 3600, 22, 5040, 30, 5184, 17, 6300, 27, 6480, 25, 6720, 28, 7560, 32, 10080, 36, 14400, 31

1

S000894

Note that each k appears only once. See S000895 and S000896 for the separate lists of m and k. This is sequence A227068 sorted and with k giving is position.

T. D. Noe, Plot of 105 pairs

T. D. Noe, Table of 105 pairs

(Mma) nn = 10^6; t3 = Table[0, {Floor[Sqrt[nn]]}]; t4 = {}; found = 0; Do[c = Length[Select[Divisors[n], # < Sqrt[n] &]]; If[c > 0 && c <= nn && t3[[c]] == 0, t3[[c]] = n; AppendTo[t4, {n, c}]; found++], {n, nn}]; t4

Cf. A227068, S000891-S000896.

nonn

T. D. Noe, May 19 2016

© Tony D Noe 2014-2016