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
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
Programs
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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);
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Mathematica
q[k_] := !PrimeQ[k] && Divisible[k-1, DivisorSigma[1, k]-k]; Select[Range[2, 6500], q] (* Amiram Eldar, Jul 26 2025 *)
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PARI
isok(n) = (n!=1) && !isprime(n) && !frac((n-1)/(sigma(n)-n)); \\ Michel Marcus, Feb 28 2019