A338786 Numbers in A166981 that are neither superior highly composite nor colossally abundant.

1, 4, 24, 36, 48, 180, 240, 720, 840, 1260, 1680, 10080, 15120, 25200, 27720, 110880, 166320, 277200, 332640, 554400, 665280, 2162160, 3603600, 7207200, 8648640, 10810800, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 698377680, 735134400, 1102701600

Offset

1,2

Comments

These are numbers both highly composite and superabundant but neither superior highly composite nor colossally abundant.

This sequence, A224078, A304234, and A304235 are mutually exclusive subsets that comprise A166981.

Superset A166981 has 449 terms; this sequence has 358, A224078 has 20, A304234 has 39, and A304235 has 32.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..358

Michael De Vlieger, Annotated plot of a(n) at (x,y) = (a(n)/A002110(A001221(a(n)), A002110(A001221(a(n)))

Eric Weisstein's World of Mathematics, Highly Composite Number

Eric Weisstein's World of Mathematics, Colossally Abundant Number

Eric Weisstein's World of Mathematics, Superabundant Number

Eric Weisstein's World of Mathematics, Superior Highly Composite Number

Formula

Complement of (the union of A002182 and A004394) and (the union of A002201 and A004490).

Example

1 is in the sequence since it is the empty product, setting records for both the number of divisors and the sum of divisors, and it is neither also superior highly composite nor colossally abundant.
2 is not in the sequence since it is both colossally abundant and superior highly composite.
4 is in the sequence since it sets a record for the divisor counting and divisor sum functions, yet it is neither superior highly composite nor colossally abundant.
20951330400 is not in the sequence since it is colossally abundant though it is an HCN and SA. etc.

Mathematica

Complement[Import["https://oeis.org/A166981/b166981.txt", "Data"][[1 ;; 449, -1]], Union[FoldList[Times, Import["https://oeis.org/A073751/b073751.txt", "Data"][[1 ;; 120, -1]] ], FoldList[Times, Import["https://oeis.org/A000705/b000705.txt", "Data"][[1 ;; 120, -1]] ] ] ] (* Program reads OEIS b-files Michael De Vlieger, Nov 09 2020 *)

Crossrefs

Cf. A189228, A002201, A002182, A004394, A004490, A166981, A224078, A304234, A304235.

Sequence in context: A007544 A333655 A189228 * A363218 A048188 A121024

Adjacent sequences: A338783 A338784 A338785 * A338787 A338788 A338789

Keyword

nonn,fini,full

Author

Michael De Vlieger, Nov 09 2020

Status

approved