%I #20 May 23 2019 14:17:52
%S 1,1,2,1,3,2,1,3,2,4,1,5,3,2,4,1,5,3,2,4,6,1,7,5,3,2,4,6,1,7,5,3,2,4,
%T 6,8,1,7,5,3,9,2,4,6,8,1,7,5,3,9,2,10,4,6,8,1,11,7,5,3,9,2,10,4,6,8,1,
%U 11,7,5,3,9,2,10,4,6,8,12,1,13,11,7,5,3,9,2,10,4,6,8,12
%N Triangular array read by rows: row n consists of the numbers k from 1 to n sorted in ascending order according to the value of f(k) = A095112(k)/k.
%C f(n) = Sum_{p prime divisor of n} Sum{i=1..v_p(n)} 1/p^i, where v_p denotes the p-adic valuation. f is injective.
%e Array begins:
%e 1
%e 1 2
%e 1 3 2
%e 1 3 2 4
%e 1 5 3 2 4
%e 1 5 3 2 4 6
%e 1 7 5 3 2 4 6
%e 1 7 5 3 2 4 6 8
%e 1 7 5 3 9 2 4 6 8
%e 1 7 5 3 9 2 10 4 6 8
%e 1 11 7 5 3 9 2 10 4 6 8
%e 1 11 7 5 3 9 2 10 4 6 8 12
%e 1 13 11 7 5 3 9 2 10 4 6 8 12
%e ...
%t f[n_]:=If[n==1,0,Plus@@(Sum[1/#[[1]]^i,{i,#[[2]]}]&)/@FactorInteger[n]]
%t row[n_]:=SortBy[Range[n],f]
%t For[n=1,n<=13,n++,r=row[n];For[i=1,i<=n,i++,WriteString["stdout",r[[i]],", "]]]
%o (PARI) f(n) = sumdiv(n, d, (1==omega(d))*(n/d)); \\ A095112
%o cmpf(na, nb) = f(na)/na-f(nb)/nb;
%o tabl(nn) = {for (n=1, nn, print(Vec(vecsort([1..n], cmpf, 1))););} \\ _Michel Marcus_, Mar 28 2019
%Y Cf. A095112, A307088, A307187.
%K nonn,tabl
%O 1,3
%A _Luc Rousseau_, Mar 23 2019