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%I #25 Sep 08 2022 08:46:09
%S 1,1,7,1,3577,1,25,8,13,1,403668223,1,833,262,19,1,27,1,793,5,45,1,
%T 1795,66,8,9,31,1,2005,1,309,32,261,4238,22490141,1,21,40,43,1,399,1,
%U 1897,262,193,1,27,1252907952,711,49,1158765,1,271259,27,129,20518072
%N a(n) = smallest number k such that sigma(k+n) - sigma(k) = k + n, or -1 if no solution exists.
%C a(p-1) = 1 for any prime p.
%C a(11) > 11*10^8. - _Derek Orr_, Sep 05 2014
%C a(35) > 88*10^7. - _Derek Orr_, Sep 05 2014
%C a(185), a(385) and a(869) > 10^11. - _Hiroaki Yamanouchi_, Sep 11 2014
%H Hiroaki Yamanouchi, <a href="/A246851/b246851.txt">Table of n, a(n) for n = 1..184</a>
%e Sequence of numbers k < 10^7 such that sigma(k+n) - sigma(k) = k + n for 1 <= n <= 10:
%e n = 1: 1, 5, 8585, 16119, ... (A067816).
%e n = 2: 1, 2, 22, 14926, 31048, 69106, 246262, 5860168, ... (A246852).
%e n = 3: 7, 6285, 4693485, ... (A246853).
%e n = 4: 1, 4, 26, 122, 146, 458, 746, 3746, 47612, ... (A246854).
%e n = 5: 3577, 14773, 2843579, ... (A246855).
%e n = 6: 1, 3, 114, 116058, 340014, ...
%e n = 7: 25, 65017, ...
%e n = 8: 8, 34, 76, 13474, 19042, ...
%e n = 9: 13, 1743, 1773, 4323, 53175, 109035, 138535, ...
%e n = 10: 1, 20, 1958, 35150, 49010, 246686, 1030046, 1240694, ...
%o (Magma) A246851:=func<n|exists(r){m: m in[1..1000000] | SumOfDivisors(m+n)-SumOfDivisors(m)eq m+n}select r else-1>; [A246851(n): n in[1..100]]
%Y Cf. A000203, A067816, A246852, A246853, A246854, A246855.
%K sign
%O 1,3
%A _Jaroslav Krizek_, Sep 05 2014
%E a(11)-a(56) from _Hiroaki Yamanouchi_, Sep 11 2014
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