cp's OEIS Frontend

A249108 Composite numbers whose sum of aliquot parts divides the sum of aliquot parts of the numbers less than or equal to n and relatively prime to n.

%I A249108 #19 Nov 14 2014 11:58:18
%S A249108 133,667,961,1007,2013,3986,5662,15979,17453,33233,46943,51101,94870,
%T A249108 101444,119045,134298,136957,179567,188897,213511,226203,246149,
%U A249108 279749,299139,306667,310157,434531,449087,449183,518459,519203
%N A249108 Composite numbers whose sum of aliquot parts divides the sum of aliquot parts of the numbers less than or equal to n and relatively prime to n.
%H A249108 Ray Chandler, <a href="/A249108/b249108.txt">Table of n, a(n) for n = 1..40</a>
%e A249108 Numbers coprime to 133 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 92, 93, 94, 96, 97, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 113, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 131, 132. The sum of their aliquot parts is 4401; sigma(133) - 133 = 27 and 4401 / 27 = 163.
%p A249108 with(numtheory): P:=proc(q) local a,k,n; for n from 2 to q do
%p A249108 if not isprime(n) then a:=0;
%p A249108 for k from 1 to n do if gcd(k,n)=1 then a:=a+sigma(k)-k; fi; od;
%p A249108 if type(a/(sigma(n)-n),integer) then print(n); fi; fi; od; end: P(10^9);
%o A249108 (PARI) lista(nn) = {forcomposite(n=1, nn, s = 0; for (i=1, n, if (gcd(n, i) == 1, s += sigma(i)-i);); if ((s % (sigma(n)-n)) == 0, print1(n, ", ")););} \\ _Michel Marcus_, Nov 07 2014
%Y A249108 Cf. A001065, A249109, A249396, A249397.
%K A249108 nonn
%O A249108 1,1
%A A249108 _Paolo P. Lava_, Oct 21 2014
%E A249108 a(10)-a(13) from _Michel Marcus_, Nov 07 2014
%E A249108 a(14)-a(31) from _Ray Chandler_, Nov 12 2014