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Start of a record-breaking run of consecutive arithmetic numbers.
0

%I #17 Jan 16 2014 10:16:24

%S 1,5,19,41,181,347,1497,4955,6026,17101,55923,80897,131729,167585,

%T 393033,673859,1484603,2761381,9220483,13694929,47390331,82626389,

%U 108980139,717512595,972975322,1333553577,2547417520,3033935561,21214519093,24441006509,261703848520

%N Start of a record-breaking run of consecutive arithmetic numbers.

%C A number is called arithmetic (A003601) if the average of its divisors is integer.

%C The run that starts at 261703848520 has length 132.

%e The first arithmetic numbers are 1, 3, 5, 6, 7, 11, hence the first two terms of the sequence are 1 and 5.

%t arQ[n_] := 0 == Mod @@ (DivisorSigma[#, n] & /@ {1,0}); r=c=n=0; While[True, If[arQ[++n], c++, If[c>r, r=c; Print@{c, n-c}]; c=0]]

%Y Cf. A003601.

%K nonn

%O 1,2

%A _Giovanni Resta_, Jan 16 2014