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A085842 Numbers k whose divisors (apart from 1 and k) sum to a prime.

%I A085842 #15 Jun 08 2025 16:15:42
%S A085842 4,6,9,10,22,25,30,34,42,49,58,60,70,78,82,84,102,118,120,121,138,142,
%T A085842 168,169,186,198,202,214,216,220,222,228,234,238,240,246,258,270,274,
%U A085842 280,282,289,294,298,348,358,360,361,364,370,372,382,390,394,406,414,438,442,444
%N A085842 Numbers k whose divisors (apart from 1 and k) sum to a prime.
%H A085842 Amiram Eldar, <a href="/A085842/b085842.txt">Table of n, a(n) for n = 1..10000</a>
%e A085842 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.
%p A085842 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;
%t A085842 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 *)
%t A085842 Select[Range[500], PrimeQ[DivisorSigma[1, #] - # - 1] &] (* _Amiram Eldar_, Dec 04 2020 *)
%o A085842 (PARI) isok(k) = isprime(sigma(k)-1-k); \\ _Michel Marcus_, Dec 04 2020
%Y A085842 Cf. A037020, A048050.
%K A085842 nonn
%O A085842 1,1
%A A085842 _Chuck Seggelin_, Jul 05 2003