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A087443 Least integer of each prime signature ordered first by sum of exponents and then by least integer value.

%I A087443 #15 Feb 19 2020 10:35:01
%S A087443 1,2,4,6,8,12,30,16,24,36,60,210,32,48,72,120,180,420,2310,64,96,144,
%T A087443 216,240,360,840,900,1260,4620,30030,128,192,288,432,480,720,1080,
%U A087443 1680,1800,2520,6300,9240,13860,60060,510510,256,384,576,864,960,1296,1440
%N A087443 Least integer of each prime signature ordered first by sum of exponents and then by least integer value.
%C A087443 A025487 in a different order.
%H A087443 Alois P. Heinz, <a href="/A087443/b087443.txt">Rows n = 0..26, flattened</a>
%e A087443 1;
%e A087443 2;
%e A087443 4,6;
%e A087443 8,12,30;
%e A087443 16,24,36,60,210;
%e A087443 32,48,72,120,180,420,2310;
%e A087443 64,96,144,216,240,360,840,900,1260,4620,30030;
%e A087443 128,192,288,432,480,720,1080,1680,1800,2520,6300,9240,13860,60060,510510;
%p A087443 b:= proc(n, i, l)
%p A087443       `if`(n=0, [mul(ithprime(t)^l[t], t=1..nops(l))],
%p A087443       `if`(i=1, b(0, 0, [l[], 1$n]), [b(n, i-1, l)[],
%p A087443       `if`(i>n, [], b(n-i, i, [l[], i]))[]]))
%p A087443     end:
%p A087443 T:= n-> sort(b(n$2, []))[]:
%p A087443 seq(T(n), n=0..10);  # _Alois P. Heinz_, Jun 13 2012
%t A087443 b[n_, i_, l_] := b[n, i, l] = If[n == 0, Join[{Product[Prime[t]^l[[t]], {t, 1, Length[l]}]}], If[i == 1, b[0, 0, Join[l, Table[1, {n}]]], Join[b[n, i - 1, l], If[i > n, {}, b[n - i, i, Append[l, i]]]]]];
%t A087443 T[n_] := Sort[b[n, n, {}]];
%t A087443 Table[T[n], {n, 0, 10}] // Flatten (* _Jean-François Alcover_, Apr 06 2017, after _Alois P. Heinz_ *)
%Y A087443 Cf. A025487, A036035, A059901, A063008, A077569, A074140 (row sums), A328524.
%K A087443 nonn,tabf
%O A087443 0,2
%A A087443 _Ray Chandler_, Sep 04 2003