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%I #4 May 13 2019 01:10:28
%S 1,1,1,2,1,1,1,1,2,1,2,3,2,2,1,1,2,1,1,1,1,1,3,1,1,2,1,3,1,2,2,4,1,1,
%T 2,2,3,1,3,1,1,3,1,1,3,1,1,1,2,1,2,2,1,4,2,2,2,1,1,3,3,3,1,4,1,1,1,2,
%U 1,2,3,1,1,1,1,1,5,1,1,2,2,1,1,3,1,1,1
%N Sorted q-signature of n.
%C Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:
%C 11 = q(1) q(2) q(3) q(5)
%C 50 = q(1)^3 q(2)^2 q(3)^2
%C 360 = q(1)^6 q(2)^3 q(3)
%C Row n is the multiset of nonzero multiplicities in the q-factorization of n. For example, row 11 is (1,1,1,1) and row 360 is (1,3,6).
%e Triangle begins:
%e {}
%e 1
%e 1 1
%e 2
%e 1 1 1
%e 1 2
%e 1 2
%e 3
%e 2 2
%e 1 1 2
%e 1 1 1 1
%e 1 3
%e 1 1 2
%e 1 3
%e 1 2 2
%e 4
%e 1 1 2
%e 2 3
%e 1 3
%e 1 1 3
%t difac[n_]:=If[n==1,{},With[{i=PrimePi[FactorInteger[n][[1,1]]]},Sort[Prepend[difac[n*i/Prime[i]],i]]]];
%t Table[Sort[Length/@Split[difac[n]]],{n,30}]
%Y Row lengths are A324923.
%Y Row sums are A196050.
%Y Row-maxima are A109129.
%Y Cf. A118914, A324922, A324924, A324931, A324934, A325608, A325609, A325613, A325614, A325660.
%K nonn,tabf
%O 1,4
%A _Gus Wiseman_, May 12 2019
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