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A181825 Members of A025487 whose prime signature is self-conjugate (as a partition).

%I A181825 #51 Feb 16 2025 08:33:13
%S A181825 1,2,12,36,120,360,1680,5040,5400,27000,36960,75600,110880,378000,
%T A181825 960960,1587600,1663200,2882880,7938000,8316000,32672640,34927200,
%U A181825 43243200,98017920,174636000,216216000,277830000,908107200,1152597600,1241560320,1470268800,1944810000
%N A181825 Members of A025487 whose prime signature is self-conjugate (as a partition).
%C A181825 A025487(n) is included iff A025487(n) = A181822(n).
%C A181825 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 A181825 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 A181825 David A. Corneth, <a href="/A181825/a181825.gp.txt">PARI-program</a>
%H A181825 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Self-ConjugatePartition.html">Self-Conjugate Partition</a>
%e A181825 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 A181825 (PARI) \\ See Corneth link \\ _David A. Corneth_, Jun 03 2020
%Y A181825 Cf. A025487, A181822, A303557.
%Y A181825 Includes subsequences A006939 and A181555.
%Y A181825 See also A181823, A181824, A181826, A181827.
%K A181825 nonn,easy
%O A181825 1,2
%A A181825 _Matthew Vandermast_, Dec 08 2010
%E A181825 a(18)-a(32) from _Amiram Eldar_, Jan 19 2019