A337686 a(n) is the least multiplier k such that n*k has twice as many divisors as n.
2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 6, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4
Offset: 1
Keywords
Examples
a(1) = 2 because 1 has 1 divisor, 1*2 has 2 divisors, so 2 is the least multiplier to apply to 1 to get twice as many divisors.
Links
- Michel Marcus, Table of n, a(n) for n = 1..10000
- Hugo Pfoertner, Illustration of ratio A007978(n) / a(n), using Plot 2.
Programs
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Mathematica
nn = 105; Do[d[i] = DivisorSigma[0, i], {i, 12 nn}]; Reap[Do[m = 2; While[d[m i] != 2 d[i], m++]; Sow[m ], {i, nn}]][[-1, -1]] (* Michael De Vlieger, Jan 10 2022 *) -
PARI
a(n) = {my(k=1); while (numdiv(n*k) != 2*numdiv(n), k++); k;}
Formula
a(n) = A129902(n)/n.
Comments