cp's OEIS Frontend

A228302 Composite squarefree numbers n such that p+d(n) divides n-d(n) for all prime factors p of n, where d(n) is the number of divisors of n.

%I A228302 #31 Sep 23 2013 06:08:23
%S A228302 4958,51653,55583,1251574,4909102,5430797,5785073,6096931,13892243,
%T A228302 14058781,14809517,16699426,27391073,32426566,32673383,38669686,
%U A228302 43459682,44762461,53638783,69836866,74975761,75226313,85607461,96973703,105139141,122864065
%N A228302 Composite squarefree numbers n such that p+d(n) divides n-d(n) for all prime factors p of n, where d(n) is the number of divisors of n.
%C A228302 Subsequence of A120944.
%H A228302 Donovan Johnson, <a href="/A228302/b228302.txt">Table of n, a(n) for n = 1..100</a>
%e A228302 Prime factors of 51653 are 7, 47 and 157 while d(51653) = 8. We have that 51653 - 8 = 51645 and 51645 / (7 + 8) =  3443, 51645 / (47 + 8) = 939 and 51645 / (157 + 8) = 313.
%p A228302 with(numtheory);  P:=proc(q) local a,i,ok,p,n;
%p A228302 for n from 1 to q do if not isprime(n) and issqrfree(n) then
%p A228302 a:=ifactors(n)[2]; ok:=1; for i from 1 to nops(a) do
%p A228302 if not type((n-tau(n))/(a[i][1]+tau(n)),integer) then ok:=0; break; fi; od;
%p A228302 if ok=1 then print(n); fi; fi; od; end: P(10^9);
%Y A228302 Cf. A000005, A228299-A228301.
%K A228302 nonn
%O A228302 1,1
%A A228302 _Paolo P. Lava_, Aug 20 2013
%E A228302 More terms from _Michel Marcus_, Sep 21 2013
%E A228302 First term deleted by _Paolo P. Lava_, Sep 23 2013