A361786 Bi-unitary arithmetic numbers: numbers for which the arithmetic mean of the bi-unitary divisors is an integer.
1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99
Offset: 1
Keywords
Examples
6 is a term since the arithmetic mean of its bi-unitary divisors, {1, 2, 3, 6}, is 3 which is an integer.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
f[p_, e_] := If[OddQ[e], (p^(e+1)-1)/((e + 1)*(p-1)), ((p^(e+1)-1)/(p-1)-p^(e/2))/e]; q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[100], q]
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PARI
is(n) = {my(f = factor(n), p, e); denominator(prod(i=1, #f~, p = f[i, 1]; e = f[i, 2]; if(e%2, (p^(e+1)-1)/((e + 1)*(p-1)), ((p^(e+1)-1)/(p-1)-p^(e/2))/e))) == 1; }
Comments