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%I #31 Feb 26 2020 09:37:01
%S 1,2,2,3,4,2,3,7,6,8,2,6,6,9,8,6,10,10,3,8,4,6,7,8,2,9,10,8,4,10,10,7,
%T 13,8,8,8,2,6,8,14,2,9,7,8,6,9,8,13,8,15,14,6,9,9,8,10,12,14,13,8,8,
%U 11,6,14,16,12,14,12,16,15,12,18,16,11,8,22
%N Integer quotients when sigma(sigma(x))/x is an integer.
%C Below n=5x10^11, q=5 and 17 quotients do not appear; smallest numbers providing integer quotients = 1, 2, 3, 4,..., 16,... are as follows: 1, 2, 8, 15, _?_, 42, 24, 60, 168, 480, 57669920, 2200380, 57120, 217278, 1058148, 7526400, ... - updated by _Jud McCranie_, Feb 08 2012
%C The above sequence is now A272930. - _Franklin T. Adams-Watters_, May 11 2016
%C See A019278 for the actual numbers x such that x | sigma(sigma(x)). - _M. F. Hasler_, Jul 03 2016
%H Jud McCranie and Giovanni Resta, <a href="/A098223/b098223.txt">Table of n, a(n) for n = 1..145</a> (first 130 terms from Jud McCranie)
%F In order of appearance the sigma(sigma(A019278(n)))/A019278(n) quotients which are by definition integers.
%p with(numtheory): A098223:=n->`if`(sigma(sigma(n)) mod n = 0, sigma(sigma(n))/n, NULL): seq(A098223(n), n=1..10^5); # _Wesley Ivan Hurt_, Oct 10 2014
%t Select[DivisorSigma[1, DivisorSigma[1, #]]/# &@ Range[10^6], IntegerQ] (* _Michael De Vlieger_, May 11 2016 *)
%o (PARI) for(n=1,1e7, sigma(sigma(n))%n||print1(sigma(sigma(n))/n",")) \\ _M. F. Hasler_, Jul 03 2016
%Y Cf. A000203, A098219-A098222, A019278, A008333, A051027, A272930.
%K nonn
%O 1,2
%A _Labos Elemer_, Oct 25 2004
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