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%I #15 Jun 28 2019 21:41:17
%S 1,4,36,48,180,720,5040,20160,25200,45360,50400,498960,665280,3603600,
%T 6486480,7207200,8648640,14414400,32432400,110270160,698377680,
%U 2095133040,2205403200,41902660800,73329656400,146659312800,240940299600,293318625600,963761198400
%N Largely composite numbers (A067128) with a unique number of divisors.
%C These are highly composite numbers (A002182) that have no other largely composite numbers with the same number of divisors.
%C The corresponding numbers of divisors d(a(n)) are 1, 3, 9, 10, 18, 30, 60, 84, 90, 100, ... (see the link for more values).
%H Amiram Eldar, <a href="/A308531/b308531.txt">Table of n, a(n) for n = 1..114</a>
%H Amiram Eldar, <a href="/A308531/a308531.txt">Table of n, a(n), d(a(n)) for n = 1..114</a>
%F A002182(k) is in the sequence if A308530(k) = 1.
%e 4 is in the sequence since it is the only largely composite number with 3 divisors.
%e 2 is not in the sequence since it has 2 divisors, the same as the next largely composite number 3.
%t s = {}; dm = 1; c = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c == 1, AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^8}]; s
%Y Cf. A000005, A002182, A067128, A308530.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jun 06 2019
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