A086486 - OEIS

%I #15 Dec 05 2013 19:56:19

%S 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,30,31,32,37,41,43,47,49,53,

%T 59,60,61,64,67,70,71,73,79,81,83,89,90,97,101,103,105,107,109,113,

%U 120,121,125,127,128,131,137,139,140,149,150,151,157,163,167

%N Numbers n such that the sum of the distinct prime divisors divides rad(n)=A007947(n).

%C Every prime power is a member.

%C Numbers with exactly two distinct prime divisors are not members of the sequence. - Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003

%C Numbers n such that A008472(n) divides A007947(n).

%H Harvey P. Dale, <a href="/A086486/b086486.txt">Table of n, a(n) for n = 1..1000</a>

%e 30 is a member. The prime divisors of 30 are 2,3 and 5 and 2+3+5 = 10, divides 30.

%e 84, however, is not a member because the sum of its distinct prime divisors (2+3+7=12) does not divide the product of its distinct prime divisors (2*3*7=42), even though 12 does divide 84. [From Harvey P. Dale, Nov 26 2011, based on a comment from Ray Chandler]

%t sdpQ[n_]:=Module[{dpds=Transpose[FactorInteger[n]][[1]]}, Divisible[ Times@@dpds,Total[dpds]]]; Select[Range[2,200],sdpQ] (* _Harvey P. Dale_, Nov 26 2011 *)

%Y Cf. A086487, A066031. A proper subset of A089352.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Jul 28 2003

%E More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003

%E Edited by _Franz Vrabec_, Sep 03 2005