A340232 a(n) is the least number with exactly 2*n bi-unitary divisors.

2, 6, 32, 24, 512, 96, 8192, 120, 131072, 1536, 2097152, 480, 33554432, 24576, 536870912, 840, 8589934592, 7776, 137438953472, 7680, 2199023255552, 6291456, 35184372088832, 3360, 562949953421312, 100663296, 9007199254740992, 122880, 144115188075855872, 124416

Offset: 1

Author

Amiram Eldar, Jan 01 2021

Keywords

• nonn

Comments

Every integer except 1 has an even number of bi-unitary divisors.

Examples

			a(1) = 2 since 2 is the least number with 2*1 = 2 bi-unitary divisors, 1 and 2.
a(2) = 6 since 6 is the least number with 2*2 = 4 bi-unitary divisors, 1, 2, 3 and 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..62

Crossrefs

Subsequence of A025487.

Cf. A222266, A286324, A293185.

Similar sequences: A005179 (all divisors), A038547 (odd divisors), A085629 (coreful divisors), A309181 (nonunitary), A340233 (exponential).

Programs

Mathematica

f[p_, e_] := If[OddQ[e], e + 1, e]; d[1] = 1; d[n_] := Times @@ (f @@@ FactorInteger[n]);  max = 10; s = Table[0, {max}]; c = 0; n = 2;  While[c < max, i = d[n]/2; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s

Formula

A286324(a(n)) = 2*n and A286324(k) != 2*n for all k < a(n).