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

1,1

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

Links

Table of n, a(n) for n=1..21.

Example

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.

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

Crossrefs

Cf. A002093, A002182, A067128, A244353.

Sequence in context: A057695 A233315 A157363 * A234732 A057805 A057796

Adjacent sequences: A308571 A308572 A308573 * A308575 A308576 A308577

Keyword

nonn,more

Author

Amiram Eldar, Jun 08 2019

Extensions

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

Status

approved