A306531 Composite numbers k such that the sum of their aliquot parts divides k-1.

4, 8, 9, 16, 25, 27, 32, 49, 64, 77, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 611, 625, 729, 841, 961, 1024, 1073, 1331, 1369, 1681, 1849, 2033, 2048, 2187, 2197, 2209, 2401, 2809, 3125, 3481, 3721, 4096, 4489, 4913, 5041, 5293, 5329, 6031, 6241

Offset: 1

Author

Paolo P. Lava, Feb 22 2019

Keywords

• nonn
• easy

Examples

			Aliquot parts of 77 are 1, 7, 11 and 78/(1+7+11) = 76/19 = 4.
		

Links

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

Crossrefs

Union of A059047 and A246547.

Cf. A203966, A306532.

Programs

Maple

with(numtheory): P:=proc(n) if not isprime(n) and frac((n-1)/(sigma(n)-n))=0 then n; fi; end: seq(P(i),i=2..6241);

Mathematica

q[k_] := !PrimeQ[k] && Divisible[k-1, DivisorSigma[1, k]-k]; Select[Range[2, 6500], q] (* Amiram Eldar, Jul 26 2025 *)

PARI

isok(n) = (n!=1) && !isprime(n) && !frac((n-1)/(sigma(n)-n)); \\ Michel Marcus, Feb 28 2019