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

%I #21 Aug 27 2022 10:27:07

%S 15,20,24,35,54,95,98,104,119,135,143,144,160,189,207,209,224,287,319,

%T 323,324,351,363,375,377,384,390,459,464,527,539,559,608,779,845,864,

%U 875,899,923,989,999,1000,1007,1029,1189,1199,1215,1280,1343,1349,1375

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

%H David A. Corneth, <a href="/A143321/b143321.txt">Table of n, a(n) for n = 1..10000</a>

%e The distinct primes dividing 24 are 2 and 3, since 24 is factored as 2^3 *3^1. 2 + 3 = 5 is a divisor of 24 + 1 = 25. So 24 is a term of this sequence.

%p with(numtheory): a:= proc(n) local f: f:=factorset(n); if `mod`(n+1, add(i, i=f))=0 then n end if end proc: seq(a(n), n=2..1200); # _Emeric Deutsch_, Aug 14 2008

%t Select[Range[2,1500],Divisible[#+1,Total[FactorInteger[#][[All,1]]]]&] (* _Harvey P. Dale_, Aug 27 2022 *)

%o (PARI) is(n) = n > 1 && (n + 1) % vecsum(factor(n)[, 1]) == 0 \\ _David A. Corneth_, Mar 10 2019

%Y Cf. A008472, A089352, A143322.

%K nonn

%O 1,1

%A _Leroy Quet_, Aug 07 2008

%E More terms from _Emeric Deutsch_, Aug 14 2008

%E More terms from _Max Alekseyev_, Mar 10 2009