cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A328518 Number of terms k in A002182 that have A001222(k) = n.

Original entry on oeis.org

1, 1, 2, 1, 3, 3, 4, 3, 3, 5, 8, 7, 8, 9, 10, 8, 9, 9, 9, 12, 11, 10, 11, 13, 13, 13, 13, 14, 16, 16, 16, 18, 18, 17, 21, 19, 18, 18, 22, 22, 23, 22, 23, 22, 25, 26, 28, 28, 27, 27, 29, 29, 30, 31, 32, 34, 30, 29, 29, 30, 31, 33, 35, 35, 32, 30, 32, 33, 31, 30, 30, 33
Offset: 0

Views

Author

David A. Corneth, Jan 04 2020

Keywords

Comments

If for every term t > 1 in A002182 there is some term t/p where p|t in A002182 then a(n) > 0 for all n.
The above hypothesis isn't true, e.g., t = A002182(815) is a counterexample. But it is surely true that a(n) > 0 for all n, see the graph of A112778. - M. F. Hasler, Jan 08 2020

Crossrefs

Cf. A001222, A002182.
Cf. A112778 (bigomega of HCNs).

Programs

  • PARI
    {my(v=v112778,c=Vec(0,vecmax(v)));for(i=2,#v,c[v[i]]++);c[1..-log(#c)\1]} \\ Does not include the leading a(0)=1. Discards log(#c) possibly inaccurate trailing terms. Vector v112778 must be defined, e.g., from b-file of A112778. - M. F. Hasler, Jan 08 2020

A328519 Terms in A002182 sorted by their Omega values (their number of prime factors counted with multiplicity).

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 36, 60, 48, 120, 180, 240, 360, 840, 1260, 720, 1680, 2520, 5040, 7560, 27720, 10080, 15120, 25200, 55440, 83160, 20160, 45360, 50400, 110880, 166320, 277200, 720720, 1081080, 221760, 332640, 498960, 554400, 1441440, 2162160, 3603600, 665280, 2882880
Offset: 1

Views

Author

David A. Corneth, Jan 04 2020

Keywords

Crossrefs

Cf. A001222 (bigomega), A002182 (Highly Composite Numbers).
Cf. A112778 (bigomega of HCNs).

Programs

  • Mathematica
    With[{s = Array[DivisorSigma[0, #] &, 3*10^6]}, SortBy[#, PrimeOmega] &@ Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]]
(* or, using the b-file at A002182: *)
Take[SortBy[Import["https://oeis.org/b002182.txt", "Data"][[All, -1]], PrimeOmega], 43] (* Michael De Vlieger, Jan 19 2020 *)
  • PARI
    vecextract(A2182,vecsort(v112778,,1)) \\ v112778=apply(bigomega,A2182[1..N]) or from b-file; A2182 must be a vector of values of A002182. - M. F. Hasler, Jan 08 2020

A328522 Largest highly composite number that has n prime factors counted with multiplicity.

Original entry on oeis.org

1, 2, 6, 12, 60, 180, 1260, 2520, 27720, 83160, 1081080, 3603600, 61261200, 698377680, 3491888400, 80313433200, 240940299600, 1686582097200, 48910880818800, 1516237305382800, 3032474610765600, 112201560598327200, 3066842656354276800, 131874234223233902400, 659371171116169512000, 30990445042459967064000
Offset: 0

Views

Author

David A. Corneth, Jan 04 2020

Keywords

Comments

These numbers are upper bounds on the largest term in A002182 that is not divisible by k for some k.

Crossrefs

Cf. A001222, A002182, A112778, A328521.

Programs

  • Mathematica
    With[{s = Take[Import["https://oeis.org/b002182.txt", "Data"][[All, -1]], 240]}, Drop[TakeWhile[#, IntegerQ], -6] &@ Table[s[[Lookup[#, n][[-1]] ]], {n, 0, Max@ Keys@ #}] &@ PositionIndex[Map[PrimeOmega, s]]] (* Michael De Vlieger, Jan 19 2020, using b-file at A002182. Caution: ensure full population of a given value of bigomega by extending scope beyond the desired number of terms. *)
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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