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a(n) = the largest number k such that floor(sigma(k)/tau(k)) = n, or 0 if no such number k exists.
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%I #8 Nov 21 2024 19:51:31

%S 2,4,8,12,0,18,24,21,30,36,40,48,45,60,56,72,63,84,90,75,96,120,108,

%T 112,0,144,110,140,0,180,160,156,136,67,116,210,240,200,198,252,175,

%U 224,208,225,288,228,0,360,336,0,172,315,0,330,272,420,294,306,0,396

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

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

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

%e 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.

%o (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]];

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

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Mar 23 2019