%I #50 Aug 17 2020 23:25:50
%S 1,2,12,36,120,360,1680,5040,5400,27000,36960,75600,110880,378000,
%T 960960,1587600,1663200,2882880,7938000,8316000,32672640,34927200,
%U 43243200,98017920,174636000,216216000,277830000,908107200,1152597600,1241560320,1470268800,1944810000
%N Members of A025487 whose prime signature is self-conjugate (as a partition).
%C A025487(n) is included iff A025487(n) = A181822(n).
%C Closed under the binary operations of GCD and LCM, since a self-conjugate partition of Omega(a(n)) (which the prime signature of these numbers is) is the concatenation of self-conjugate hooks of decreasing size while moving downward and to the right in the Ferrers diagram, and the GCD (or LCM) of two terms a(i) and a(j) is obtained by taking the smaller (or larger, respectively) of the corresponding hooks. For example, GCD(a(8),a(11)) = GCD(5040,36960) = 1680 = a(7), and LCM(a(8),a(11)) = 110880 = a(13). The two binary operations make the set {a(n)} into a lattice order. - _Richard Peterson_, May 29 2020
%H David A. Corneth, <a href="/A181825/b181825.txt">Table of n, a(n) for n = 1..11879</a> (first 578 terms from Amiram Eldar, terms <= 10^70)
%H David A. Corneth, <a href="/A181825/a181825.gp.txt">PARI-program</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Self-ConjugatePartition.html">Self-Conjugate Partition</a>
%e A025487(11) = 36 = 2^2*3^2 has a prime signature of (2,2), which is a self-conjugate partition; hence, 36 is included in the sequence.
%o (PARI) \\ See Corneth link \\ _David A. Corneth_, Jun 03 2020
%Y Cf. A025487, A181822, A303557.
%Y Includes subsequences A006939 and A181555.
%Y See also A181823, A181824, A181826, A181827.
%K nonn,easy
%O 1,2
%A _Matthew Vandermast_, Dec 08 2010
%E a(18)-a(32) from _Amiram Eldar_, Jan 19 2019