cp's OEIS Frontend

A228301 Composite squarefree numbers n such that p-d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.

%I A228301 #16 Sep 23 2013 06:08:31
%S A228301 6,10,14,15,35,70,154,190,322,385,442,595,682,2737,3619,14986,15314,
%T A228301 19019,24817,26767,33626,78387,85034,130169,155363,166934,189727,
%U A228301 214107,225029,238901,243217,285934,381547,395219,415679,417989,455609,466193,544918
%N A228301 Composite squarefree numbers n such that p-d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.
%C A228301 Subsequence of A120944.
%H A228301 Donovan Johnson, <a href="/A228301/b228301.txt">Table of n, a(n) for n = 1..500</a>
%e A228301 Prime factors of 19019 are 7, 11, 13 and 19 while d(19019) = 16. We have that 19019 + 16 = 19035 and 19035 / (7 - 16) =  -2115, 19035 / (11 - 16) =  -3807, 19035 / (13 - 16) = -6345 and 19035 / (19 - 16) = 6345.
%p A228301 with (numtheory); P:=proc(q) local a,b,c,i,ok,p,n;
%p A228301 for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A228301 for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
%p A228301 else if not type((n+tau(n))/(a[i][1]-tau(n)),integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);
%Y A228301 Cf. A000005, A228299, A228300, A228302.
%K A228301 nonn
%O A228301 1,1
%A A228301 _Paolo P. Lava_, Aug 20 2013
%E A228301 First term deleted by _Paolo P. Lava_, Sep 23 2013