A340233 - OEIS

%I #13 Jan 02 2021 04:50:16

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

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

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

%C See the link for more values of this sequence.

%H Amiram Eldar, <a href="/A340233/b340233.txt">Table of n, a(n) for n = 1..12</a>

%H Amiram Eldar, <a href="/A340233/a340233.txt">Table of n, a(n) for n = 1..100</a> (given by prime factorizations)

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

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

%t 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 *)

%Y Subsequence of A025487.

%Y Cf. A049419, A318278, A322791.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Jan 01 2021