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%I #9 Jul 03 2026 22:25:56
%S 20,98,148,164,180,216,260,289,332,388,432,538,556,652,964,972
%N Integers x such that there exist four integers 0<y<=z<=t<=w such that sigma(x)^2*psi(x)^2 = x^4 + y^4 + z^4 + t^4 + w^4.
%C The numbers x, y, z, t and w form a sigma^2*psi^2-quartic quintuple.
%H S. I. Dimitrov, <a href="https://hal.science/hal-05303937">On σψ-quadratic k-tuples and related generalizations</a>, hal-05303937, 2025.
%H S. I. Dimitrov, <a href="https://github.com/Stoyan16/Sigma-2-psi-2-quartic-quintuples/blob/main/A397440">Python program</a> (GitHub)
%e (98, 32, 50, 78, 162) is such a quintuple because sigma(98)^2 * psi(98)^2 = 171^2 * 168^2 = 98^4 + 32^4 + 50^4 + 78^4 + 162^4.
%o (Python) # See Links.
%Y Cf. A000203, A001615, A386225, A391536, A397304.
%K nonn,hard,more
%O 1,1
%A _S. I. Dimitrov_, Jun 25 2026