A306532 Composite numbers k such that the sum of their aliquot parts divides k+1.
21, 115, 329, 731, 2133, 2171, 6821, 7379, 8357, 13987, 19521, 24331, 24881, 29491, 46001, 50579, 56789, 79421, 103729, 117409, 125159, 137881, 174109, 176661, 226859, 235721, 257291, 357769, 492071, 499091, 560537, 584021, 704791, 776341, 822857, 850607, 908981
Offset: 1
Examples
Aliquot parts of 21 are 1, 3, 7 and 22/(1+3+7) = 22/11 = 2.
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..100000);
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Mathematica
Select[Range[10^6],CompositeQ[#]&&Mod[#+1,Total[Most[Divisors[#]]]]==0&] (* Harvey P. Dale, Jul 28 2024 *)
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PARI
isok(n) = (n!=1) && !isprime(n) && !frac((n+1)/(sigma(n)-n)); \\ Michel Marcus, Feb 28 2019