A340840 Union of the highly composite and superabundant numbers.

1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160, 2882880

Offset

1,2

Comments

Numbers m that set records in A000005 and numbers k that set records for the ratio A000203(k)/k, sorted, with duplicates removed.

All terms are in A025487, since all terms in A002182 and A004394 are products of primorials P in A002110.

For numbers that are highly composite but not superabundant, see A308913; for numbers that are superabundant but not highly composite, see A166735. - Jon E. Schoenfield, Jun 14 2021

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Annotated scatterplot of a(n) = A301414(x) * A002110(y) at (x, y) showing the intersection A166981 of A002182 and A004394, and the intersection A224078 of A002201 and A004490.

Mathematica

(* Load the function f[] at A025487, then: *) Block[{t = Union@ Flatten@ f[15], a = {}, b = {}, d = 0, s = 0}, Do[(If[#2 > d, d = #2; AppendTo[a, #1]]; If[#3/#1 > s, s = #3/#1; AppendTo[b, #1]]) & @@ Flatten@ {t[[i]], DivisorSigma[{0, 1}, t[[i]]]}, {i, Length@ t}]; Union[a, b]]

Crossrefs

Cf. A000005, A000203, A027750, A002110.

Supersets: A025487, A055932.

Subsets: A002182, A002201, A004394, A004490, A166735, A166981, A168263, A189228, A224078, A304234, A304235, A308913, A333655, A338786.

Sequence in context: A094348 A242298 A002182 * A077006 A166981 A004394

Adjacent sequences: A340837 A340838 A340839 * A340841 A340842 A340843

Keyword

nonn

Author

Michael De Vlieger, Jan 27 2021

Status

approved