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

1,1

Links

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

Example

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.

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;

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 *)

Prog

(PARI) isok(k) = isprime(sigma(k)-1-k); \\ Michel Marcus, Dec 04 2020

Crossrefs

Cf. A037020, A048050.

Sequence in context: A215478 A118693 A084668 * A356135 A131220 A332618

Adjacent sequences: A085839 A085840 A085841 * A085843 A085844 A085845

Keyword

nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 05 2003

Status

approved