A087443 - OEIS

%I #15 Feb 19 2020 10:35:01

%S 1,2,4,6,8,12,30,16,24,36,60,210,32,48,72,120,180,420,2310,64,96,144,

%T 216,240,360,840,900,1260,4620,30030,128,192,288,432,480,720,1080,

%U 1680,1800,2520,6300,9240,13860,60060,510510,256,384,576,864,960,1296,1440

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

%C A025487 in a different order.

%H Alois P. Heinz, <a href="/A087443/b087443.txt">Rows n = 0..26, flattened</a>

%e 1;

%e 2;

%e 4,6;

%e 8,12,30;

%e 16,24,36,60,210;

%e 32,48,72,120,180,420,2310;

%e 64,96,144,216,240,360,840,900,1260,4620,30030;

%e 128,192,288,432,480,720,1080,1680,1800,2520,6300,9240,13860,60060,510510;

%p b:= proc(n, i, l)

%p       `if`(n=0, [mul(ithprime(t)^l[t], t=1..nops(l))],

%p       `if`(i=1, b(0, 0, [l[], 1$n]), [b(n, i-1, l)[],

%p       `if`(i>n, [], b(n-i, i, [l[], i]))[]]))

%p     end:

%p T:= n-> sort(b(n$2, []))[]:

%p seq(T(n), n=0..10);  # _Alois P. Heinz_, Jun 13 2012

%t 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 T[n_] := Sort[b[n, n, {}]];

%t Table[T[n], {n, 0, 10}] // Flatten (* _Jean-François Alcover_, Apr 06 2017, after _Alois P. Heinz_ *)

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

%K nonn,tabf

%O 0,2

%A _Ray Chandler_, Sep 04 2003