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

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%I A340232 #13 Jan 03 2021 02:37:57
%S A340232 2,6,32,24,512,96,8192,120,131072,1536,2097152,480,33554432,24576,
%T A340232 536870912,840,8589934592,7776,137438953472,7680,2199023255552,
%U A340232 6291456,35184372088832,3360,562949953421312,100663296,9007199254740992,122880,144115188075855872,124416
%N A340232 a(n) is the least number with exactly 2*n bi-unitary divisors.
%C A340232 Every integer except 1 has an even number of bi-unitary divisors.
%H A340232 Amiram Eldar, <a href="/A340232/b340232.txt">Table of n, a(n) for n = 1..62</a>
%F A340232 A286324(a(n)) = 2*n and A286324(k) != 2*n for all k < a(n).
%e A340232 a(1) = 2 since 2 is the least number with 2*1 = 2 bi-unitary divisors, 1 and 2.
%e A340232 a(2) = 6 since 6 is the least number with 2*2 = 4 bi-unitary divisors, 1, 2, 3 and 6.
%t A340232 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
%Y A340232 Subsequence of A025487.
%Y A340232 Cf. A222266, A286324, A293185.
%Y A340232 Similar sequences: A005179 (all divisors), A038547 (odd divisors), A085629 (coreful divisors), A309181 (nonunitary), A340233 (exponential).
%K A340232 nonn
%O A340232 1,1
%A A340232 _Amiram Eldar_, Jan 01 2021