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Integers k such that the equation A034699(k)=x has more than one solution in the range [prevprime(k), nextprime(k)].
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%I #34 Jan 05 2020 21:47:24

%S 4180,4199,43355,43384,68400,68425,162150,162197,326781,326830,448477,

%T 448514,1013948,1013985,1060790,1060851,1357216,1357299,1373904,

%U 1373951,1568800,1568853,1928880,1928927,2313685,2313744,8752880,8752951,11555804,11555901,11962832,11962935,16062201,16062280,23120064,23120153

%N Integers k such that the equation A034699(k)=x has more than one solution in the range [prevprime(k), nextprime(k)].

%C Is it always true that a(2*n) - a(2*n-1) = A034699(2*n) = A034699(2*n-1)? - _I. V. Serov_, Jun 23 2019

%H L. Joris Perrenet, <a href="/A308752/b308752.txt">Table of n, a(n) for n = 1..108</a>

%e A034699(4180) = A034699(4199) = 19 in the range [4177, 4201].

%e A034699(23120064) = A034699(23120153) = 89 in [23120039, 23120171]. - _I. V. Serov_, Jun 23 2019

%o (PARI) lppf(n) = if(1==n, n, my(f=factor(n)); vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2]))); \\ A034699

%o lista(nn) = {for (n=1, nn, my(p = prime(n), q = nextprime(p+1)); my(v = vector(q-p-1, k, lppf(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], ", "));););););}

%Y Cf. A007917 (prevprime), A007918 (nextprime), A034699.

%K nonn

%O 1,1

%A _Michel Marcus_, Jun 22 2019

%E a(35)-a(36) from _I. V. Serov_, Jun 23 2019