A308617 Integers i such that the equation A088387(i) = p has N > 1 solutions in the interval prevprime(i)..nextprime(i).

140, 147, 621, 630, 2184, 2197, 2511, 2520, 3230, 3249, 3740, 3757, 4180, 4199, 5750, 5775, 9975, 10000, 19635, 19652, 26600, 26625, 30600, 30625, 40040, 40053, 43355, 43384, 45900, 45927, 50232, 50255, 50600, 50625, 64515, 64538, 67320, 67337, 68400, 68425

Offset

1,1

Comments

Conjecture: N = 2. Checked up to 10^8.

Links

Table of n, a(n) for n=1..40.

Example

Between primes 139 and 149: A088387(140) = A088387(147) = 7.
Between primes 619 and 631: A088387(621) = A088387(630) = 3.
Between primes 8752871 and 8752987: A088387(8752880) = A088387(8752951) = 71 and A088387(8752926) = A088387(8752967) = 41.
Between primes 33622489 and 33622607: A088387(33622507) = A088387(33622600) = 31.

Mathematica

A088387[n_] := MaximalBy[FactorInteger[n], Power @@ # &][[1, 1]]; A034699[n_] := If[n == 1, 1, Max[#[[1]]^#[[2]] & /@ FactorInteger@n]]; t = Table[Table[A088387[n], {n, Prime[k], Prime[k + 1]-1}], {k, 2, 12000}  ]; duplicates = Select[t, Not@DuplicateFreeQ[#] &]; a = {}; pickFrom[list_] := Do[If[Count[list, list[[k]]] > 1 , a = Append[a, k - 1 + First[list]]], {k, 2, Length[list]}]; pickFrom /@ duplicates; a (* Jianglin Luo, Dec 01 2023 *)

Prog

(MATLAB)
n = 0; ip = 0;
for m = 1:oo
if isprime(m) ip = ip + 1; end
if A088387(m) == m & m > 1
  for i = A007917(ip):A007918(ip)
   for j = A007917(ip):A007918(ip)
    if A088387(i) == A088387(j) & i ~= j
     n = n + 1; a(n) = i;
    end
   end
  end
end
end
(PARI) plppf(n) = if(1==n, 1, my(f=factor(n), p=0); isprimepower(vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2])), &p); (p)); \\ A088387
lista(nn) = {for (n=1, nn, my(p = prime(n), q = nextprime(p+1)); my(v = vector(q-p-1, k, plppf(k+p)), vs = vecsort(v, , 8)); if (#v != #vs, for (i=1, #vs, my(vx = select(x->(x==vs[i]), v, 1)); if (#vx > 1, for (j=1, #vx, print1(p+vx[j], ", ")); ); ); ); ); } \\ Michel Marcus, Jun 27 2019

Crossrefs

Cf. A007917 (prevprime), A007918 (nextprime), A088387, A034699, A308752 (analog), A038610.

Sequence in context: A108317 A252963 A114825 * A353074 A224982 A256085

Adjacent sequences: A308614 A308615 A308616 * A308618 A308619 A308620

Keyword

nonn

Author

I. V. Serov & Michel Marcus, Jun 25 2019

Status

approved