More Primal Code Sequences

[Jon Awbrey]

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SeqFans,

My brain is in a somewhat hazy vacation mode,
and I'm having to compute these by brute farce
manual calculation, so I'd truly appreciate any
comments or corrections.

Jon Awbrey

%I A109297
%S A109297 1,2,9,12,18,40,112,125,250,352,360,540,600,675,832,
%T A109297 1008,1125,1350,1500,2176,2250
%N A109297 Primal codes of finite permutations on positive integers.
%C A109297 A finite permutation is a bijective mapping from a finite
           set to itself, counting the empty mapping as a permutation
           of the empty set.
%e A109297 Writing (prime(i))^j as i:j, we have the following table:
%e A109297 Primal Codes of Finite Permutations on Positive Integers
%e A109297 ` `1 = { }
%e A109297 ` `2 = 1:1
%e A109297 ` `9 = 2:2
%e A109297 ` 12 = 1:2 2:1
%e A109297 ` 18 = 1:1 2:2
%e A109297 ` 40 = 1:3 3:1
%e A109297 `112 = 1:4 4:1
%e A109297 `125 = 3:3
%e A109297 `250 = 1:1 3:3
%e A109297 `352 = 1:5 5:1
%e A109297 `360 = 1:3 2:2 3:1
%e A109297 `540 = 1:2 2:3 3:1
%e A109297 `600 = 1:3 2:1 3:2
%e A109297 `675 = 2:3 3:2
%e A109297 `832 = 1:6 6:1
%e A109297 1008 = 1:4 2:2 4:1
%e A109297 1125 = 2:2 3:3
%e A109297 1350 = 1:1 2:3 3:2
%e A109297 1500 = 1:2 2:1 3:3
%e A109297 2176 = 1:7 7:1
%e A109297 2250 = 1:1 2:2 3:3
%Y A109297 Cf. A076954, A106177, A108352, A108371, A109298, A109301.
%O A109297 0
%K A109297 nonn,new
%A A109297 Jon Awbrey (jawbrey(AT)att.net), Jul 08 2005

%I A109298
%S A109298 1,2,9,18,125,250,1125,2250,2401,4802,21609,43218,300125,600250,
%T A109298 2701125,5402250
%N A109298 Primal codes of finite idempotent functions on positive integers.
%C A109298 Finite idempotent functions are identity maps on finite subsets,
           counting the empty function as the idempotent on the empty set.
%e A109298 Writing (prime(i))^j as i:j, we have the following table of examples:
%e A109298 Primal Codes of Finite Idempotent Functions on Positive Integers
%e A109298 ` ` ` 1 = { }
%e A109298 ` ` ` 2 = 1:1
%e A109298 ` ` ` 9 = ` ` 2:2
%e A109298 ` ` `18 = 1:1 2:2
%e A109298 ` ` 125 = ` ` ` ` 3:3
%e A109298 ` ` 250 = 1:1 ` ` 3:3
%e A109298 ` `1125 = ` ` 2:2 3:3
%e A109298 ` `2250 = 1:1 2:2 3:3
%e A109298 ` `2401 = ` ` ` ` ` ` 4:4
%e A109298 ` `4802 = 1:1 ` ` ` ` 4:4
%e A109298 ` 21609 = ` ` 2:2 ` ` 4:4
%e A109298 ` 43218 = 1:1 2:2 ` ` 4:4
%e A109298 `300125 = ` ` ` ` 3:3 4:4
%e A109298 `600250 = 1:1 ` ` 3:3 4:4
%e A109298 2701125 = ` ` 2:2 3:3 4:4
%e A109298 5402250 = 1:1 2:2 3:3 4:4
%Y A109298 Cf. A076954, A106177, A108352, A108371, A108297, A109301.
%O A109298 0
%K A109298 nonn,new
%A A109298 Jon Awbrey (jawbrey(AT)att.net), Jul 06 2005

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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