A229276 - OEIS

%I #20 Jun 14 2022 10:46:28

%S 6,10,15,66,145,231,435,1221,11571,99093,105502,292434,449854,585429,

%T 643858,968014,1372494,1787091,1939434,4659114,5524014,5654334,

%U 6250371,6974007,19495374,19821714,28488039,34701369,46183893,81133734,213352233,230140869

%N 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 Subsequence of A120944.

%H Kevin P. Thompson, <a href="/A229276/b229276.txt">Table of n, a(n) for n = 1..62</a>

%e Prime factors of 435 are 3, 5, 29 and sigma(435) = 720, tau(435) = 8.

%e 435 + 720 = 1155 and 1155 / (3 - 8) = -231, 1155 / (5 - 8) = -385, 1155 / (29 - 8) = 55.

%p with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;

%p for n from 2 to q do  if not isprime(n) then a:=ifactors(n)[2]; ok:=1;

%p for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;

%p 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 Cf. A000005, A000203, A228299-A228302, A229273-A229275.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Sep 19 2013

%E a(21)-a(33) from _Giovanni Resta_, Sep 20 2013

%E First term deleted by _Paolo P. Lava_, Sep 23 2013