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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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

Crossrefs

Subsequence of A025487.

Cf. A222266, A286324, A293185.

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

Sequence in context: A342396 A376052 A190958 * A109243 A223586 A212762

Adjacent sequences: A340229 A340230 A340231 * A340233 A340234 A340235

Keyword

nonn

Author

Amiram Eldar, Jan 01 2021

Status

approved