A324991 a(n) = the largest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.

2, 4, 8, 12, 0, 18, 24, 21, 30, 36, 40, 48, 45, 60, 56, 72, 63, 84, 90, 75, 96, 120, 108, 112, 0, 144, 110, 140, 0, 180, 160, 156, 136, 67, 116, 210, 240, 200, 198, 252, 175, 224, 208, 225, 288, 228, 0, 360, 336, 0, 172, 315, 0, 330, 272, 420, 294, 306, 0, 396

Offset: 1

Author

Jaroslav Krizek, Mar 23 2019

Keywords

• nonn

Comments

Floor(sigma(n)/tau(n)) = floor(A000203(n)/A000005(n)) = A057022(n) for n >= 1.

a(n) = 0 for numbers n = 5, 25, 29, 47, 50, 53, 59, 83, 89, ...

Examples

			For n = 4; number 12 is the largest number k with floor(sigma(k)/tau(k)) = 4; floor(sigma(12)/tau(12)) = floor(28/6) = 4.
		

Crossrefs

Cf. A000005, A000203, A057022, A162538, A324990.

Programs

Magma

[Max([n: n in[1..10^5] | Floor(SumOfDivisors(n)/ NumberOfDivisors(n)) eq k]): k in [1..4]] cat [0] cat [Max([n: n in[1..10^5] | Floor(SumOfDivisors(n)/ NumberOfDivisors(n)) eq k]): k in [6..24]];