A380969 a(n) is the smallest k such that tau(k^2 + 1) is equal to 2^n, where tau = A000005 and a(n) = -1 if no such k exists.
0, 1, 3, 13, 47, 307, 2163, 17557, 191807, 1413443, 16485763, 169053487
Offset: 0
Programs
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Mathematica
a[n_]:=Module[{k=0}, While[DivisorSigma[0, k^2+1]!=2^n, k++]; k]; Array[a, 9,0] (* Stefano Spezia, Feb 10 2025 *) -
PARI
a(n) = my(k=0); while (numdiv(k^2+1) != 2^n, k++); k; \\ Michel Marcus, Feb 09 2025
Formula
a(n) = A353008(2^(n-1)) for n > 0.
Extensions
a(10)-a(11) from Stefano Spezia, Feb 12 2025