A234801 Start of a record-breaking run of consecutive arithmetic numbers.

1, 5, 19, 41, 181, 347, 1497, 4955, 6026, 17101, 55923, 80897, 131729, 167585, 393033, 673859, 1484603, 2761381, 9220483, 13694929, 47390331, 82626389, 108980139, 717512595, 972975322, 1333553577, 2547417520, 3033935561, 21214519093, 24441006509, 261703848520

Offset

1,2

Comments

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

The run that starts at 261703848520 has length 132.

Links

Table of n, a(n) for n=1..31.

Example

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

Mathematica

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]]

Crossrefs

Cf. A003601.

Sequence in context: A033622 A091568 A147307 * A089148 A098319 A022267

Adjacent sequences: A234798 A234799 A234800 * A234802 A234803 A234804

Keyword

nonn

Author

Giovanni Resta, Jan 16 2014

Status

approved