A097975 - OEIS

%I #20 Dec 23 2017 04:20:06

%S 0,2,3,2,5,3,7,0,3,5,11,0,13,7,5,0,17,0,19,5,7,11,23,0,5,13,0,7,29,0,

%T 31,0,11,17,7,0,37,19,13,0,41,7,43,11,0,23,47,0,7,0,17,13,53,0,11,0,

%U 19,29,59,0,61,31,0,0,13,11,67,17,23,0,71,0,73,37,0,19,11,13,79,0,0,41,83

%N a(n) is the prime divisor of n which is >= sqrt(n), or 0 if there is no such prime divisor.

%C Sequence also is the sum of distinct prime divisors of n which are >= sqrt(n). At most one prime divisor of n is >= square root of n.

%H Diana Mecum, <a href="/A097975/b097975.txt">Table of n, a(n) for n = 1..1000</a>

%t Do[l = Select[Select[Divisors[n], PrimeQ], # >= Sqrt[n]&]; If[Length[l] == 0, Print[0], Print[l[[1]]]], {n, 1, 50}] (* _Ryan Propper_, Jul 24 2005 *)

%t Array[Select[FactorInteger[#][[All, 1]], Function[p, p >= Sqrt@ #]] /. {{} -> {0}, {1} -> {0}} &, 83][[All, 1]] (* _Michael De Vlieger_, Dec 22 2017 *)

%o (PARI) a(n) = sumdiv(n, d, if (isprime(d) && (d^2 >= n), d)); \\ _Michel Marcus_, Dec 23 2017

%Y Cf. A097974.

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 07 2004

%E More terms from _Ryan Propper_, Jul 24 2005

%E More terms from _Stefan Steinerberger_, Jan 21 2006

%E Further terms from _Diana L. Mecum_, Jun 15 2007