A229275 - OEIS

%I #17 Jan 16 2018 02:45:02

%S 10778,16471,17353,439453,1304443,3719678,9234253,17270678,20512335,

%T 21179143,50706307,77292313,95506557,103081993,104707029,140419077,

%U 240626953,287947933,822767689,982374757,1608154233,1918313911,2219891947,2471777007,2632397677

%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.

%e Prime factors of 10778 are 2, 17, 317 and sigma(10778) = 17172, tau(10778) = 8.

%e 10778 + 17172 = 27950 and 27950 / (2 + 8) = 2795, 27950 / (17 + 8) = 1118, 27950 / (317 + 8) = 86.

%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 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, A229274, A229276.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Sep 19 2013

%E a(4) corrected and a(7)-a(26) by _Giovanni Resta_, Sep 20 2013

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