cp's OEIS Frontend

A249109 Composite numbers whose sum of aliquot parts divides the sum of the aliquot parts of the numbers less than or equal to n and not relatively prime to n.

%I A249109 #18 Nov 14 2014 12:00:07
%S A249109 15,26,27,38,76,194,531,1445,1501,2923,2988,4427,4499,4769,5817,7831,
%T A249109 9523,10602,12412,14963,16117,24863,26768,29041,29329,30229,36577,
%U A249109 45246,49817,58483,58823,71165,75469,76273,79799,83429,86941,94037
%N A249109 Composite numbers whose sum of aliquot parts divides the sum of the aliquot parts of the numbers less than or equal to n and not relatively prime to n.
%H A249109 Ray Chandler, <a href="/A249109/b249109.txt">Table of n, a(n) for n = 1..64</a>
%e A249109 Numbers not coprime to 15 are 3, 5, 6, 9, 10, 12, 15. Then, sigma(3) - 3 = 1, sigma(5) - 5 = 1, sigma(6) - 6 = 6, sigma(9) - 9 = 4, sigma(10) - 10 = 8, sigma(12) - 12 = 16, sigma(15) - 15 = 9; their sum is 1 + 1 + 6 + 4 + 8 + 16 + 9 = 45 and 45 / 9 = 5.
%p A249109 with(numtheory): P:=proc(q) local a,k,n; for n from 2 to q do
%p A249109 if not isprime(n) then a:=0;
%p A249109 for k from 1 to n do if gcd(k,n)>1 then a:=a+sigma(k)-k; fi; od;
%p A249109 if type(a/(sigma(n)-n),integer) then print(n); fi; fi; od; end: P(10^9);
%o A249109 (PARI) lista(nn) = {forcomposite(n=1, nn, if (sum(k=1, n, if (gcd(k,n) !=1, sigma(k)-k)) % (sigma(n) - n) == 0, print1(n, ", ")););} \\ _Michel Marcus_, Nov 09 2014
%Y A249109 Cf. A001065, A249108, A249396, A249397.
%K A249109 nonn
%O A249109 1,1
%A A249109 _Paolo P. Lava_, Oct 21 2014
%E A249109 a(22)-a(38) from _Michel Marcus_, Nov 09 2014