A385238 Numbers k such that A224787(k) - k is a square.

8, 16, 20, 25, 95, 169, 221, 234, 295, 312, 323, 410, 543, 1027, 1681, 3071, 3419, 3721, 4183, 4352, 6649, 7448, 7979, 8188, 9047, 9200, 10108, 11203, 12769, 15732, 16240, 20303, 22819, 25351, 26291, 28769, 32761, 33728, 42880, 51198, 51338, 52206, 53613, 55303, 56800, 63731, 65567, 71531, 77550

Offset: 1

Author

Will Gosnell and Robert Israel, Jul 28 2025

Keywords

• nonn

Comments

Numbers k such that the sum of the cubes of the prime factors of k, counted with multiplicity, is k plus a square.

Includes p^2 for p in A027862.

Examples

			a(3) = 20 = 2^2 * 5 is a term because 2*2^3 + 5^3 - 20 = 121 is a square.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2451

Crossrefs

Cf. A027862, A224787, A386623, A386640.

Programs

Maple

filter:= proc(n) local t;
   issqr(add(t[1]^3*t[2], t=ifactors(n)[2]) - n)
end proc:
select(filter, [$1..10^5]);