A386246 Composite numbers k such that A075254(k) is a square.

27, 108, 171, 240, 456, 603, 744, 936, 988, 1424, 1702, 1737, 1820, 1899, 1904, 1989, 2166, 2261, 2366, 2817, 2873, 3283, 3553, 3681, 3728, 3784, 3852, 3894, 4266, 4437, 4700, 4923, 4975, 5005, 5008, 5073, 5117, 5193, 5278, 5356, 5418, 5820, 6050, 6486, 6576, 6627, 6651, 6775, 7947, 8250, 9116

Offset: 1

Author

Will Gosnell and Robert Israel, Jul 16 2025

Keywords

• nonn

Comments

Composite numbers k such that k + sopfr(k) is a square, where sopfr(k) is the sum of prime factors of k with multiplicity.

Contains no semiprimes.

Includes 9*p if p is a prime of the form (x^2-6)/10 where x == 4 or 6 (mod 10).

Is this sequence disjoint from A386245?

Examples

			a(3) = 171 is a term because 171 = 3^2 * 19 is composite and 171 + 3 + 3 + 19 = 196 = 14^2 is a square.
		

Links

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

Crossrefs

Cf. A075254, A386245.

Programs

Maple

filter:= proc(n) local t;
 if isprime(n) then return false fi;
 issqr(n + add(t[1]*t[2], t=ifactors(n)[2]))
end proc:
select(filter, [$4..10000]);