A088949 Composite numbers k such that (A006530(k) + A020639(k))/2 is an integer that divides k; special terms of A088948.

4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 105, 121, 125, 128, 169, 231, 243, 256, 289, 315, 343, 361, 512, 525, 529, 625, 627, 693, 729, 735, 841, 897, 935, 945, 961, 1024, 1155, 1331, 1369, 1575, 1581, 1617, 1681, 1729, 1849, 1881, 2048, 2079, 2187, 2197, 2205, 2209

Offset: 1

Author

Labos Elemer, Nov 20 2003

Keywords

• nonn

Examples

			k = 315 = 3*3*5*7 (composite); (3 + 7)/2 = 5, which divides k.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A020639, A088948, A088595, A046687.

Programs

Mathematica

q[k_] := CompositeQ[k] && Module[{p = FactorInteger[k][[;;, 1]], m}, m = (p[[1]] + p[[-1]]); EvenQ[m] && Divisible[k, m/2]]; Select[Range[2500], q] (* Amiram Eldar, Mar 01 2025 *)

PARI

lista(nn) = {forcomposite(n=1, nn, my(f = factor(n)[,1], x = (vecmin(f) + vecmax(f))/2); if ((denominator(x)==1) && !(n % x), print1(n, ", ")););} \\ Michel Marcus, Jul 09 2018

Extensions

Edited by Jon E. Schoenfield, Jul 08 2018

More terms from Michel Marcus, Jul 09 2018