A390179 Numbers that can be represented as p^r + q^s with 4 distinct odd primes p, q, r, s.

18138, 19004, 21720, 23666, 28974, 41196, 46598, 67460, 79456, 80322, 83038, 84984, 85728, 90292, 96314, 102514, 107916, 120630, 128778, 147046, 157632, 161394, 163238, 163248, 165684, 165964, 167910, 173218, 181948, 185440, 190842, 193954, 211704, 222186, 227002

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) == 0 (mod 2).

Example

a(1) = 18138 = 7^5 + 11^3.

Maple

N:= 10^6: # for terms <= N
P:= select(isprime, [seq(i, i=3..floor(N^(1/3)), 2)]):
R:= NULL:
for p in P do
  for r in P do
    if r = p then next fi;
    v:= p^r;
    if v > N then break fi;
    for q in P do
      if q >= p then break fi;
      if q = r then next fi;
      for s in P do
        if member(s, {p, q, r}) then next fi;
        w:= v + q^s;
        if w > N then next fi;
        R:= R, w
od od od od:
sort(convert({R}, list)); # Robert Israel, Oct 30 2025

Crossrefs

Subsequence of A390066.

Cf. A390188.

Sequence in context: A224571 A251832 A250639 * A205242 A172936 A025029

Adjacent sequences: A390176 A390177 A390178 * A390180 A390181 A390182

Keyword

nonn

Author

Hugo Pfoertner, Oct 29 2025

Status

approved