A085842 Numbers k whose divisors (apart from 1 and k) sum to a prime.
4, 6, 9, 10, 22, 25, 30, 34, 42, 49, 58, 60, 70, 78, 82, 84, 102, 118, 120, 121, 138, 142, 168, 169, 186, 198, 202, 214, 216, 220, 222, 228, 234, 238, 240, 246, 258, 270, 274, 280, 282, 289, 294, 298, 348, 358, 360, 361, 364, 370, 372, 382, 390, 394, 406, 414, 438, 442, 444
Offset: 1
Keywords
Examples
102 is a member since the divisors of 102 are {1, 2, 3, 6, 17, 34, 51, 102} and 2 + 3 + ... + 51 = 113, a prime.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
with(numtheory); b := []; for n from 3 to 2000 do t1 := divisors(n); t2 := convert(t1,list); t3 := add(t2[i],i=1..nops(t2)); if isprime(t3-1-n) then b := [op(b),n]; fi; od: b;
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Mathematica
f[n_]:=Plus@@Divisors[n]-n-1; lst={};Do[a=f[n];If[PrimeQ[a],AppendTo[lst,n]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 21 2009 *) Select[Range[500], PrimeQ[DivisorSigma[1, #] - # - 1] &] (* Amiram Eldar, Dec 04 2020 *) -
PARI
isok(k) = isprime(sigma(k)-1-k); \\ Michel Marcus, Dec 04 2020