cp's OEIS Frontend

A325614 Unsorted q-signature of n.

%I A325614 #5 May 13 2019 01:10:22
%S A325614 1,1,1,2,1,1,1,2,1,2,1,3,2,2,2,1,1,1,1,1,1,3,1,2,1,1,3,1,2,2,1,4,2,1,
%T A325614 1,3,2,3,1,3,1,1,3,1,1,2,1,1,1,2,2,1,4,1,2,2,2,3,1,1,3,3,4,1,2,1,1,1,
%U A325614 3,2,1,1,1,1,1,1,5,2,2,1,1,3,1,1,3,1,1
%N A325614 Unsorted q-signature of n.
%C A325614 Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:
%C A325614    11 = q(1) q(2) q(3) q(5)
%C A325614    50 = q(1)^3 q(2)^2 q(3)^2
%C A325614   360 = q(1)^6 q(2)^3 q(3)
%C A325614 Row n lists the nonzero multiplicities in the q-factorization of n, in order of q-index. For example, row 11 is (1,1,1,1) and row 360 is (6,3,1).
%e A325614 Triangle begins:
%e A325614   {}
%e A325614   1
%e A325614   1 1
%e A325614   2
%e A325614   1 1 1
%e A325614   2 1
%e A325614   2 1
%e A325614   3
%e A325614   2 2
%e A325614   2 1 1
%e A325614   1 1 1 1
%e A325614   3 1
%e A325614   2 1 1
%e A325614   3 1
%e A325614   2 2 1
%e A325614   4
%e A325614   2 1 1
%e A325614   3 2
%e A325614   3 1
%e A325614   3 1 1
%t A325614 difac[n_]:=If[n==1,{},With[{i=PrimePi[FactorInteger[n][[1,1]]]},Sort[Prepend[difac[n*i/Prime[i]],i]]]];
%t A325614 Table[Length/@Split[difac[n]],{n,30}]
%Y A325614 Row lengths are A324923.
%Y A325614 Row sums are A196050.
%Y A325614 Row-maxima are A109129.
%Y A325614 Cf. A118914, A324922, A324924, A324931, A324934, A325608, A325609, A325613, A325615, A325660.
%K A325614 nonn,tabf
%O A325614 1,4
%A A325614 _Gus Wiseman_, May 12 2019