cp's OEIS Frontend

A229273 Composite squarefree numbers n such that p-tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).

%I A229273 #21 Jan 16 2018 02:44:53
%S A229273 6,10,15,22,78,138,273,483,3243,3913,104377,477337,1537627,1904487,
%T A229273 2508961,3326829,3716167,5148949,6154017,6686113,11521842,14355679,
%U A229273 16872583,25165777,28029883,31232337,32403342,50725419,57396469,68815381,86850249,98242959
%N A229273 Composite squarefree numbers n such that p-tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).
%C A229273 Subsequence of A120944.
%e A229273 Prime factors of 273 are 3, 7, 13 and sigma(273) = 448, tau(273) = 8.
%e A229273 273 - 448 = -175 and (-175) / (3 - 8) = 35, (-175) / (7 - 8) = 175, (-175) / (13 - 8) = -35.
%p A229273 with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;
%p A229273 for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
%p A229273 for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
%p A229273 else if not type((n-sigma(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(2*10^6);
%Y A229273 Cf. A000005, A000203.
%Y A229273 Cf. A228299, A228300, A228301, A228302, A229274, A229275, A229276.
%K A229273 nonn
%O A229273 1,1
%A A229273 _Paolo P. Lava_, Sep 19 2013
%E A229273 a(20)-a(33) from _Giovanni Resta_, Sep 20 2013
%E A229273 First term deleted by _Paolo P. Lava_, Sep 23 2013