A363483 a(n) is the least k that has exactly n divisors whose arithmetic derivative is odd.

1, 2, 15, 6, 18, 405, 30, 162, 945, 90, 1458, 295245, 210, 450, 25515, 810, 10395, 455625, 630, 1062882, 31185, 7290, 4050, 156905298045, 1890, 354375, 18600435, 3150, 280665, 114383962274805, 5670, 36450, 135135, 590490, 1506635235, 3189375, 6930, 101250, 922640625, 5314410, 22050

Offset

0,2

Comments

a(n) is the least k such that A353235(k) = n.

a(n) <= 3^(2*n-1) for n >= 1.

Links

Robert Israel, Table of n, a(n) for n = 0..250

Example

a(3) = 6 because A353235(6) = 3.

Maple

P:= [seq(ithprime(i), i=2..10)]:V:= Array(0..100):
for i from 0 to 100 do V[i]:= infinity od:
Agenda:= {seq([i], i=0..99)}:
f:= proc(L) option remember;
   local Lp, t, s;
   if nops(L) = 1 then ceil(L[1]/2)
   else Lp:= L[1..-2];
        t:= L[-1];
        procname(Lp)*(t+1) + mul(s+1, s=Lp)*ceil(t/2) - 2*procname(Lp)*ceil(t/2);
   fi;
end:
Process:= proc(L)
  local v, x, v2, t, i;
  global Agenda, V;
  v:= f(L);
  if v > 100 then return fi;
  x:= mul(P[i]^L[i], i=1..nops(L));
  if x < V[v] then V[v]:= x; printf("%d %d\n", v, x) fi;
  v2:= v + mul(t+1, t=L);
  if v2 <= 100 and 2*x < V[v2] then V[v2]:= 2*x; printf("%d %d\n", v2, 2*x) fi;
  Agenda:= Agenda union {seq([op(L), t], t=1..L[-1])}
end proc;
Process := proc (L) local v, x, v2, t, i; global Agenda, V;
 v := f(L);
 if 100 < v then return  end if;
 x := mul(P[i]^L[i], i = 1 .. nops(L));
 if x < V[v] then V[v] := x;  end if;
 v2 := v+mul(t+1, t = L);
 if v2 <= 100 and 2*x < V[v2] then V[v2] := 2*x; p end if;
 Agenda := Agenda union {seq([op(L), t], t = 1   .. L[-1])}
end proc:
while Agenda <> {} do
  L0:= Agenda[1];
  Agenda:= subsop(1=NULL, Agenda);
  Process(L0);
od:
convert(V, list);

Crossrefs

Cf. A353235.

Sequence in context: A104773 A371895 A371340 * A128759 A066582 A111329

Adjacent sequences: A363480 A363481 A363482 * A363484 A363485 A363486

Keyword

nonn

Author

Robert Israel, Jun 05 2023

Status

approved