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A340840
Union of the highly composite and superabundant numbers.
1
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, 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]]
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jan 27 2021
STATUS
approved