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A308617
Integers i such that the equation A088387(i) = p has N > 1 solutions in the interval prevprime(i)..nextprime(i).
1
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
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.
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 *)
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
KEYWORD
nonn
AUTHOR
I. V. Serov & Michel Marcus, Jun 25 2019
STATUS
approved