cp's OEIS Frontend

A325615 Sorted q-signature of n.

%I A325615 #4 May 13 2019 01:10:28
%S A325615 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 A325615 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 A325615 1,2,3,1,1,1,1,1,5,1,1,2,2,1,1,3,1,1,1
%N A325615 Sorted q-signature of n.
%C A325615 Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:
%C A325615    11 = q(1) q(2) q(3) q(5)
%C A325615    50 = q(1)^3 q(2)^2 q(3)^2
%C A325615   360 = q(1)^6 q(2)^3 q(3)
%C A325615 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 A325615 Triangle begins:
%e A325615   {}
%e A325615   1
%e A325615   1 1
%e A325615   2
%e A325615   1 1 1
%e A325615   1 2
%e A325615   1 2
%e A325615   3
%e A325615   2 2
%e A325615   1 1 2
%e A325615   1 1 1 1
%e A325615   1 3
%e A325615   1 1 2
%e A325615   1 3
%e A325615   1 2 2
%e A325615   4
%e A325615   1 1 2
%e A325615   2 3
%e A325615   1 3
%e A325615   1 1 3
%t A325615 difac[n_]:=If[n==1,{},With[{i=PrimePi[FactorInteger[n][[1,1]]]},Sort[Prepend[difac[n*i/Prime[i]],i]]]];
%t A325615 Table[Sort[Length/@Split[difac[n]]],{n,30}]
%Y A325615 Row lengths are A324923.
%Y A325615 Row sums are A196050.
%Y A325615 Row-maxima are A109129.
%Y A325615 Cf. A118914, A324922, A324924, A324931, A324934, A325608, A325609, A325613, A325614, A325660.
%K A325615 nonn,tabf
%O A325615 1,4
%A A325615 _Gus Wiseman_, May 12 2019