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

1, 2, 4, 6, 8, 12, 30, 16, 24, 36, 60, 210, 32, 48, 72, 120, 180, 420, 2310, 64, 96, 144, 216, 240, 360, 840, 900, 1260, 4620, 30030, 128, 192, 288, 432, 480, 720, 1080, 1680, 1800, 2520, 6300, 9240, 13860, 60060, 510510, 256, 384, 576, 864, 960, 1296, 1440

Offset: 0

Author

Ray Chandler, Sep 04 2003

Keywords

• nonn
• tabf

Comments

A025487 in a different order.

Examples

			1;
2;
4,6;
8,12,30;
16,24,36,60,210;
32,48,72,120,180,420,2310;
64,96,144,216,240,360,840,900,1260,4620,30030;
128,192,288,432,480,720,1080,1680,1800,2520,6300,9240,13860,60060,510510;
		

Links

• Alois P. Heinz, Rows n = 0..26, flattened

Crossrefs

Cf. A025487, A036035, A059901, A063008, A077569, A074140 (row sums), A328524.

Programs

Maple

b:= proc(n, i, l)
      `if`(n=0, [mul(ithprime(t)^l[t], t=1..nops(l))],
      `if`(i=1, b(0, 0, [l[], 1$n]), [b(n, i-1, l)[],
      `if`(i>n, [], b(n-i, i, [l[], i]))[]]))
    end:
T:= n-> sort(b(n$2, []))[]:
seq(T(n), n=0..10);  # Alois P. Heinz, Jun 13 2012

Mathematica

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[n_] := Sort[b[n, n, {}]];
Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Apr 06 2017, after Alois P. Heinz *)