A309181 Least number with exactly n nonunitary divisors.

1, 4, 8, 16, 24, 36, 48, 256, 72, 1024, 180, 144, 216, 16384, 288, 65536, 360, 576, 3072, 900, 864, 1296, 720, 2304, 1080, 67108864, 2592, 268435456, 1440, 9216, 196608, 5184, 2160, 17179869184, 2880, 36864, 10368, 3600, 6300, 1099511627776, 4320, 20736, 6480

Offset: 0

Author

Amiram Eldar, Jul 15 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A005179, A048105, A309141.

Programs

Mathematica

nud[n_] := DivisorSigma[0, n] - 2^PrimeNu[n]; m = 24; c = 0; s = Table[0, {m + 1}]; k = 1; While[c < m + 1, n = nud[k]; If[n <= m && s[[n + 1]] == 0, c++; s[[n + 1]] = k]; k++]; s

PARI

nnud(n) = numdiv(n) - 2^omega(n); \\ A048105
a(n) = my(k=1); while (nnud(k) != n, k++); k; \\ Michel Marcus, Jul 17 2019

Formula

A048105(a(n)) = n and A048105(k) != n for all k < a(n).

a(n) <= 2^(n+1).