A386640 Numbers k such that k + A224787(k) is a square.

1, 225, 270, 1900, 4988, 5656, 6120, 8704, 11180, 16588, 17710, 19228, 24475, 28449, 29458, 32330, 34606, 38088, 39292, 40221, 41181, 42476, 48545, 48640, 53795, 56832, 57288, 64975, 78793, 84925, 86242, 117116, 124135, 128478, 129673, 134044, 136224, 136896, 147149, 150528, 168055, 183141

Offset

1,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..3000

Example

a(3) = 270 = 2 * 3^3 * 5 is a term because 270 + 2^3 + 3 * 3^3 + 5^3 =  484 = 22^2 is a square.

Maple

filter:= proc(n) local t;
   issqr(n + add(t[1]^3*t[2], t=ifactors(n)[2]))
end proc:
select(filter, [$1..10^6]);

Mathematica

lim=184000; f[{p_, e_}]:=e*p^3; a224787[k_]:=If[k==1, 0, Total[f/@FactorInteger[k]]]; q[k_]:=IntegerQ[Sqrt[k+a224787[k]]]; Select[Range[lim], q[#]&] (* James C. McMahon, Jul 30 2025 *)

Crossrefs

Cf. A224787, A385238, A386246, A386257, A386623.

Sequence in context: A345806 A044871 A202005 * A395013 A359598 A207639

Adjacent sequences: A386637 A386638 A386639 * A386641 A386642 A386643

Keyword

nonn

Author

Will Gosnell and Robert Israel, Jul 27 2025

Status

approved