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

Author

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

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1148

Crossrefs

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

Programs

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

Maple

A88387:= proc(n) local F,j;
  F:= ifactors(n)[2];
  F[max[index](map(t -> t[1]^t[2],F)),1]
end proc:
R:= NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= nextprime(q);
  L:= [$(q+1)..(p-1)];
  V:= map(A88387,L);
  S:= select(t -> numboccur(t,V) > 1, convert(V,set));
  J:= select(i -> member(V[i],S),[$1..p-q-1]);
  count:= count+nops(J);
  R:= R, op(L[J]);
  q:= p;
od:
R; # Robert Israel, Jun 20 2024

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 *)

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