A308574 Numbers between a pair of consecutive highly abundant numbers (A002093) having the same sum of divisors as the lesser one.

672, 2016, 69300, 146160, 207900, 1627920, 8316000, 9828000, 38253600, 60147360, 105814800, 158004000, 726818400, 95935039200, 191870078400, 2206505901600, 3463953292800, 3800093497200, 4413011803200, 7600186994400, 8826023606400

Offset: 1

Author

Amiram Eldar, Jun 08 2019

Keywords

• nonn
• more

Comments

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.

Analogous to A244353 as A002093 is analogous to A002182.

No more terms below 10^10.

a(22) > 10^13. - Giovanni Resta, Jul 02 2019

Examples

			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.
		

Crossrefs

Cf. A002093, A002182, A067128, A244353.

Programs

Mathematica

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

Extensions

a(14)-a(21) from Giovanni Resta, Jul 02 2019