A306621 Highly abundant numbers that are powerful.

1, 4, 8, 16, 36, 72, 108, 144, 216, 288, 1800, 3600, 7200

Offset: 1

Author

Amiram Eldar, Mar 01 2019

Keywords

• nonn
• fini
• full

Comments

Alaoglu and Erdős proved that 7200 is the last term.

Intersection of A001694 and A002093.

Links

• Leonidas Alaoglu and Paul Erdős, On highly composite and similar numbers, Transactions of the American Mathematical Society, Vol. 56, No. 3 (1944), pp. 448-469.

Crossrefs

Cf. A001694, A002093.

Programs

Mathematica

seq={1}; sm = 0; Do[s = DivisorSigma[1, n]; If[s>sm, sm = s; If[ Min @  FactorInteger[n][[;;, 2]] > 1, AppendTo[seq, n]]], {n, 2, 72000}]; seq