A181825 - OEIS

A181825

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

1, 2, 12, 36, 120, 360, 1680, 5040, 5400, 27000, 36960, 75600, 110880, 378000, 960960, 1587600, 1663200, 2882880, 7938000, 8316000, 32672640, 34927200, 43243200, 98017920, 174636000, 216216000, 277830000, 908107200, 1152597600, 1241560320, 1470268800, 1944810000

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OFFSET

1,2

COMMENTS

A025487(n) is included iff A025487(n) = A181822(n).

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

LINKS

David A. Corneth, Table of n, a(n) for n = 1..11879 (first 578 terms from Amiram Eldar, terms <= 10^70)

David A. Corneth, PARI-program

Eric Weisstein's World of Mathematics, Self-Conjugate Partition

EXAMPLE

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.

PROG

(PARI) \\ See Corneth link \\ David A. Corneth, Jun 03 2020

CROSSREFS

Cf. A025487, A181822, A303557.

Includes subsequences A006939 and A181555.

See also A181823, A181824, A181826, A181827.