A370935 a(n) is the first term of A351048 with n prime factors, counted with multiplicity, or 0 if there is no such term.

1, 0, 9, 8, 189, 72, 160, 128, 384, 1152, 3456, 6912, 10240, 46080, 55296, 32768, 98304, 294912, 884736, 4423680, 3538944, 13107200, 27262976, 73400320, 41943040, 254803968, 226492416, 1132462080, 2038431744, 1811939328, 9059696640, 2147483648, 6442450944, 19327352832, 57982058496, 289910292480

Offset

0,3

Comments

a(n) is the first number k, if any, such that A001222(k) = n and A000005(k) divides A003415(k).

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Formula

a(2^k - 1) = 2^(2^k - 1) for k >= 2.

Example

a(4) = 189 because 189 = 3^3 * 7 has 4 prime factors and A000005(189) = 8 divides A003415(189) = 216, and no smaller number works.

Maple

children:= proc(r) local L, x, p, q, t, R;
  x:= r[1];
  L:= r[2];
  t:= L[-1];
  p:= t[1]; q:= nextprime(p);
  if t[2]=1 then t:= [q, 1];
  else t:= [p, t[2]-1], [q, 1]
  fi;
  R:= [x*q/p, [op(L[1..-2]), t]];
  if nops(L) >= 2 then
    p:= L[-2][1];
    q:= L[-1][1];
    if L[-2][2]=1 then t:= [q, L[-1][2]+1]
    else t:= [p, L[-2][2]-1], [q, L[-1][2]+1]
    fi;
    R:= R, [x*q/p, [op(L[1..-3]), t]]
  fi;
  [R]
end proc:
f:= proc(n)
uses priqueue;
local pq, t, x, V, F;
initialize(pq);
insert([-2^n, [[2, n]]], pq);
do
  V:= extract(pq);
  x:= -V[1]; F:= V[2];
  if (x * add(t[2]/t[1], t=F)) mod mul(t[2]+1, t=F) = 0
     then return(x) fi;
  for t in children(V) do insert(t, pq) od;
od;
end proc:
1, 0, seq(f(n), n=2..40);

Crossrefs

Cf. A000005, A001222, A003415, A351048.

Sequence in context: A082201 A357880 A038298 * A013439 A180680 A165398

Adjacent sequences: A370932 A370933 A370934 * A370936 A370937 A370938

Keyword

nonn

Author

Robert Israel, May 06 2024

Status

approved