A306621 Highly abundant numbers that are powerful.

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

Offset

1,2

Comments

Alaoglu and Erdős proved that 7200 is the last term.

Intersection of A001694 and A002093.

Links

Table of n, a(n) for n=1..13.

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.

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

Crossrefs

Cf. A001694, A002093.

Sequence in context: A214035 A040014 A141069 * A144687 A278377 A065605

Adjacent sequences: A306618 A306619 A306620 * A306622 A306623 A306624

Keyword

nonn,fini,full

Author

Amiram Eldar, Mar 01 2019

Status

approved