A390734 Primes whose fifth power are sums of fifth powers of seven distinct primes.

1709, 2843, 4027, 4513, 4519, 4861, 5023, 5479

Offset

1,1

Comments

a(9) > 10000.

Links

Table of n, a(n) for n=1..8.

Fang, How can we find all integer solutions where the fifth powers of a prime can be expressed as sums of fifth powers of seven distinct primes? (in Chinese).

Example

1709^5 = 1567^5+1373^5+719^5+503^5+431^5+367^5+349^5.
2843^5 = 2731^5+1933^5+1459^5+709^5+509^5+271^5+31^5.
4027^5 = 3301^5+3169^5+3037^5+2411^5+1481^5+859^5+569^5.
4513^5 = 3673^5+3347^5+3313^5+3041^5+2473^5+1979^5+1087^5.
4519^5 = 4409^5+2447^5+2293^5+2267^5+1319^5+1283^5+101^5.
4861^5 = 4513^5+3329^5+3217^5+2423^5+1381^5+601^5+197^5.
5023^5 = 4013^5+4007^5+3911^5+2767^5+1993^5+1693^5+1039^5.
5479^5 = 5209^5+3691^5+3019^5+2357^5+2339^5+1721^5+1543^5.

Mathematica

f[p_]:=(pp=Prime@Range[2, PrimePi@p-1]^5; IntegerPartitions[p^5, {7}, pp]^(1/5)); Do[v=f[p]; If[v!={}, Print[{p, f[p]}]], {p, Prime@Range@PrimePi@6000}]

Crossrefs

Cf. A000040, A000584, A114923.

Sequence in context: A345782 A157287 A029559 * A222553 A345516 A345769

Adjacent sequences: A390731 A390732 A390733 * A390735 A390736 A390737

Keyword

nonn,hard,more

Author

Zhining Yang, Feb 27 2026

Status

approved