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 A325615 Sorted q-signature of n. 5
 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, 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, 1, 2, 3, 1, 1, 1, 1, 1, 5, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:    11 = q(1) q(2) q(3) q(5)    50 = q(1)^3 q(2)^2 q(3)^2   360 = q(1)^6 q(2)^3 q(3) 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). LINKS EXAMPLE Triangle begins:   {}   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 2   2 3   1 3   1 1 3 MATHEMATICA difac[n_]:=If[n==1, {}, With[{i=PrimePi[FactorInteger[n][[1, 1]]]}, Sort[Prepend[difac[n*i/Prime[i]], i]]]]; Table[Sort[Length/@Split[difac[n]]], {n, 30}] CROSSREFS Row lengths are A324923. Row sums are A196050. Row-maxima are A109129. Cf. A118914, A324922, A324924, A324931, A324934, A325608, A325609, A325613, A325614, A325660. Sequence in context: A327659 A327519 A287917 * A029434 A156281 A002217 Adjacent sequences:  A325612 A325613 A325614 * A325616 A325617 A325618 KEYWORD nonn,tabf AUTHOR Gus Wiseman, May 12 2019 STATUS approved

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Last modified April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)