A396917 - OEIS

A396917

Integers x such that there exist four integers 0<y<=z<=t<=w such that sigma(x)^2*psi(x)*phi(x) = x^4 + y^4 + z^4 + t^4 + w^4.

8, 164, 178, 202, 240, 600, 1440, 1576, 1620, 1764, 1772, 2352, 2560, 3044, 3096, 3314, 3368, 3840, 4682, 4736, 4772, 5512, 5672, 6002, 6124, 6640, 6898, 7128, 7152, 7328, 7858, 8434, 8488, 8584, 8688

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The numbers x, y, z, t and w form a sigma^2*psi*phi-quartic quintuple.

a(36), if it exists, is > 10^4. - Lyle Blosser, Jul 26 2026

LINKS

Table of n, a(n) for n=1..35.

Lyle Blosser, File showing RHS values for submitted x-values through a(35), 2026.

S. I. Dimitrov, Python program (GitHub).

EXAMPLE

(164, 12, 56, 84, 176) is such a quintuple because sigma(164)^2 * psi(164) * phi(164) = 294^2 * 252 * 80 = 164^4 + 12^4 + 56^4 + 84^4 + 176^4.

PROG

(Python) # See Links.

CROSSREFS

Cf. A000010, A000203, A001615, A386225, A391536.

Sequence in context: A299075 A299840 A353777 * A230916 A221078 A205577

Adjacent sequences: A396914 A396915 A396916 * A396918 A396919 A396920

KEYWORD

nonn,hard,more

AUTHOR

S. I. Dimitrov, Jun 10 2026

EXTENSIONS

a(16)-a(29) from Lyle Blosser, Jul 16 2026

a(30)-a(35) from Lyle Blosser, Jul 18 2026

Missing a(27) inserted by Lyle Blosser, Jul 26 2026

STATUS

approved