A397301 - OEIS

A397301

Integers x such that there exist four integers 0<x<=y<=z and 0<t<=w such that sigma(x)*psi(x)^2 = sigma(y)*psi(y)^2 = sigma(z)*psi(z)^2 = x^3 + y^3 + z^3 + t^3 + w^3.

%I #9 Jun 25 2026 19:16:47

%S 24,30,62,174,216,238,357,420,756,1146,3240,3382

%N Integers x such that there exist four integers 0<x<=y<=z and 0<t<=w such that sigma(x)*psi(x)^2 = sigma(y)*psi(y)^2 = sigma(z)*psi(z)^2 = x^3 + y^3 + z^3 + t^3 + w^3.

%C The numbers x, y, z, t and w form a sigma*psi^2-cubic 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-cubic-quintuples/blob/main/A397301">Python program</a> (GitHub)

%e (174, 190, 323, 5, 94) is such a quintuple because sigma(174) * psi(174)^2 = sigma(190) * psi(190)^2 = sigma(323) * psi(323)^2 = 360 * 360^2 = 174^3 + 190^3 + 323^3 + 5^3 + 94^3.

%o (Python) # See Links.

%Y Cf. A000203, A001615, A003328, A386378, A391535, A396564, A396407, A397251.

%K nonn,more

%O 1,1

%A _S. I. Dimitrov_, Jun 20 2026