cp's OEIS Frontend

A387291 Integers x such that there exist two numbers y,z with x <= y <= z such that psi(x) = psi(y) = psi(z) = (x + y + z)/2.

%I A387291 #35 Sep 04 2025 14:56:11
%S A387291 2,4,6,8,16,18,28,32,44,54,64,70,105,110,128,150,162,165,182,200,238,
%T A387291 240,256,280,310,315,364,382,468,486,512,520,585,590,644,735,750,780,
%U A387291 790,795,800,1000,1024,1034,1162,1246,1260,1274,1410,1434,1456,1458,1472,1540,1575
%N A387291 Integers x such that there exist two numbers y,z with x <= y <= z such that psi(x) = psi(y) = psi(z) = (x + y + z)/2.
%C A387291 The numbers x, y and z form a psi-amicable triple.
%H A387291 S. I. Dimitrov, <a href="https://arxiv.org/abs/2508.02318">On psi-amicable numbers and their generalizations</a>, arXiv:2508.02318 [math.NT], 2025.
%e A387291 2 is in the sequence since psi(2) = 3 = (2 + 2 + 2)/2.
%e A387291 28 is in the sequence since psi(28) = psi(33) = psi(35) = 48 = (28 + 33 + 35)/2.
%o A387291 (PARI) mypsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
%o A387291 isok(k) = my(vk=invpsi(mypsi(k))); vk = select(x->x>=k, vk); if (#vk, my(x = 1); for (y=x, #vk, for (z=y, #vk, if (apsi(k) == (vk[x]+vk[y]+vk[z])/2, return(1););););); \\ _Michel Marcus_, Sep 04 2025
%Y A387291 Cf. A001615, A385852, A386726, A386901, A386933, A387292, A387486.
%K A387291 nonn,new
%O A387291 1,1
%A A387291 _S. I. Dimitrov_, Aug 25 2025