A340233 a(n) is the least number with exactly n exponential divisors.

1, 4, 16, 36, 65536, 144, 18446744073709551616, 576, 1296, 589824

Offset

1,2

Comments

a(11) = 2^(2^10) has 309 digits and is too large to be included in the data section.

See the link for more values of this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..12

Amiram Eldar, Table of n, a(n) for n = 1..100 (given by prime factorizations)

Formula

A049419(a(n)) = n and A049419(k) != n for all k < a(n).

Example

a(2) = 4 since 4 is the least number with 2 exponential divisors, 2 and 4.

Mathematica

f[p_, e_] := DivisorSigma[0, e]; d[1] = 1; d[n_] := Times @@ (f @@@ FactorInteger[n]);  max = 6; s = Table[0, {max}]; c = 0; n = 1;  While[c < max, i = d[n]; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s (* ineffective for n > 6 *)

Crossrefs

Subsequence of A025487.

Cf. A049419, A318278, A322791.

Similar sequences: A005179 (all divisors), A038547 (odd divisors), A085629 (coreful divisors), A309181 (nonunitary), A340232 (bi-unitary).

Sequence in context: A030158 A054246 A173545 * A080709 A256322 A080855

Adjacent sequences: A340230 A340231 A340232 * A340234 A340235 A340236

Keyword

nonn

Author

Amiram Eldar, Jan 01 2021

Status

approved