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

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

Offset: 1

Author

Amiram Eldar, Jan 01 2021

Keywords

• nonn

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.

Examples

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

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)

Crossrefs

Subsequence of A025487.

Cf. A049419, A318278, A322791.

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

Programs

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 *)

Formula

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