A143322 Positive integers k whose sum of distinct prime divisors divides k-1.

6, 21, 28, 36, 50, 96, 99, 216, 225, 301, 325, 352, 400, 441, 486, 495, 496, 576, 630, 676, 697, 784, 847, 925, 1225, 1296, 1333, 1521, 1536, 1587, 1695, 1701, 1792, 1909, 2025, 2041, 2133, 2145, 2500, 2601, 2624, 2916, 2926, 3025, 3200, 3220, 3276, 3456

Offset: 1

Author

Leroy Quet, Aug 07 2008

Keywords

• nonn

Examples

			The distinct primes dividing 28 are 2 and 7, since 28 is factored as 2^2 * 7^1. 2 + 7 = 9 is a divisor of 28 - 1 = 27. So 28 is included in this sequence.
		

Links

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

Crossrefs

Cf. A008472, A089352, A143321.

Programs

Maple

with(numtheory): a:=proc(n) local f: f:= factorset(n): if `mod`(n-1, add(f[i], i=1..nops(f)))=0 then n else end if end proc: seq(a(n),n=2..4000); # Emeric Deutsch, Aug 16 2008

Mathematica

Select[Range[2,5000],Divisible[#-1,Total[Transpose[FactorInteger[#]][[1]]]]&] (* Harvey P. Dale, Aug 03 2014 *)

PARI

isok(k) = (k!=1) && (((k-1) % vecsum(factor(k)[,1])) == 0); \\ Michel Marcus, Dec 04 2020

Extensions

Extended by Emeric Deutsch, Aug 16 2008