A306492 Numbers k such that sigma(k) - 3k is prime.

3600, 17424, 22500, 32400, 72900, 291600, 345744, 360000, 476100, 518400, 562500, 656100, 685584, 756900, 1040400, 1382976, 1411344, 1742400, 1904400, 1988100, 2073600, 2250000, 2340900, 2624400, 3027600, 3111696, 4161600, 4284900, 5760000, 6051600, 6170256, 6200100, 6969600

Offset: 1

Author

Jan Koornstra, Feb 19 2019

Keywords

• nonn

Examples

			The divisors of 3600 are {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600}. sigma(3600) - 3 * 3600 = 12493 - 10800 = 1693, which is prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A037020, A064271.

Programs

Maple

with(numtheory): b := []: for n from 3 to 1000000 do t1 := divisors(n); t2 := convert(t1, list); t3 := add(t2[i], i=1..nops(t2)); if isprime(t3-3*n) then b := [op(b), n]; fi; od: b;

Mathematica

f[n_]:=Plus@@Divisors[n]-3*n; lst={}; Do[a=f[n]; If[PrimeQ[a], AppendTo[lst, n]], {n, 9!}]; lst
Select[Range[1000000], DivisorSigma[1,#] > 3*# && PrimeQ[DivisorSigma[1,#] - 3*#] &] (* Vaclav Kotesovec, Feb 23 2019 *)

PARI

isok(n) = isprime(sigma(n) - 3*n); \\ Michel Marcus, Feb 19 2019

Extensions

More terms from Michel Marcus, Feb 19 2019