cp's OEIS Frontend

A228299 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 A228299 #19 Sep 23 2013 06:08:50
%S A228299 21098,134930,343027,361730,387127,751394,793595,1344517,1430449,
%T A228299 1579394,1794854,3542797,5022254,7930117,9241627,12122947,21089129,
%U A228299 21928717,49825117,70233329,78795074,90079589,95208734,110995807,124648303,124964219,144871634
%N A228299 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 A228299 Subsequence of A120944.
%H A228299 Donovan Johnson, <a href="/A228299/b228299.txt">Table of n, a(n) for n = 1..100</a>
%e A228299 Prime factors of 21098 are 2, 7, 11 and 137 while d(21098) = 16. We have that 21098 + 16 = 21114 and 21114 / (2 + 16) =  1173, 21114 / (7 + 16) = 918, 21114 / (11 + 16) = 782 and 21114 / (137 + 16) = 138.
%p A228299 with (numtheory); P:=proc(q) local a,i,ok,n;
%p A228299 for n from 1 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A228299 for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
%p A228299 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 A228299 Cf. A000005, A228300-A228302.
%K A228299 nonn
%O A228299 1,1
%A A228299 _Paolo P. Lava_, Aug 20 2013
%E A228299 More terms from _Michel Marcus_, Sep 21 2013
%E A228299 Deleted first term from _Paolo P. Lava_, Sep 23 2013