login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers between a pair of consecutive highly abundant numbers (A002093) having the same sum of divisors as the lesser one.
0

%I #8 Jul 02 2019 15:28:56

%S 672,2016,69300,146160,207900,1627920,8316000,9828000,38253600,

%T 60147360,105814800,158004000,726818400,95935039200,191870078400,

%U 2206505901600,3463953292800,3800093497200,4413011803200,7600186994400,8826023606400

%N Numbers between a pair of consecutive highly abundant numbers (A002093) having the same sum of divisors as the lesser one.

%C Define "largely abundant numbers" to be numbers k such that sigma(k) >= sigma(j) for all j < k. This sequence gives all the largely abundant numbers that are not highly abundant numbers.

%C Analogous to A244353 as A002093 is analogous to A002182.

%C No more terms below 10^10.

%C a(22) > 10^13. - _Giovanni Resta_, Jul 02 2019

%e 672 is in the sequence since 660 < 672 < 720, (660, 720) are a pair of consecutive highly abundant numbers, and sigma(672) = sigma(660) = 2016.

%t s={}; sm=0; Do[s1=DivisorSigma[1,n]; If[s1==sm, AppendTo[s,n]]; If[s1>sm, sm=s1], {n,1,10^5}]; s

%Y Cf. A002093, A002182, A067128, A244353.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Jun 08 2019

%E a(14)-a(21) from _Giovanni Resta_, Jul 02 2019