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Positive integers k whose sum of distinct prime divisors divides k-1.
2

%I #16 Dec 04 2020 09:24:33

%S 6,21,28,36,50,96,99,216,225,301,325,352,400,441,486,495,496,576,630,

%T 676,697,784,847,925,1225,1296,1333,1521,1536,1587,1695,1701,1792,

%U 1909,2025,2041,2133,2145,2500,2601,2624,2916,2926,3025,3200,3220,3276,3456

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

%H Amiram Eldar, <a href="/A143322/b143322.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p 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

%t Select[Range[2,5000],Divisible[#-1,Total[Transpose[FactorInteger[#]][[1]]]]&] (* _Harvey P. Dale_, Aug 03 2014 *)

%o (PARI) isok(k) = (k!=1) && (((k-1) % vecsum(factor(k)[,1])) == 0); \\ _Michel Marcus_, Dec 04 2020

%Y Cf. A008472, A089352, A143321.

%K nonn

%O 1,1

%A _Leroy Quet_, Aug 07 2008

%E Extended by _Emeric Deutsch_, Aug 16 2008