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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A348632 Nonexponential highly composite numbers: where the number of nonexponential divisors (A160097) increases to a record.

Original entry on oeis.org

1, 6, 12, 24, 30, 60, 120, 210, 240, 360, 420, 720, 840, 1260, 1680, 2520, 3360, 5040, 7560, 9240, 10080, 15120, 18480, 25200, 27720, 36960, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 480480, 498960, 554400, 665280, 720720, 1081080, 1441440
Offset: 1

Views

Author

Amiram Eldar, Oct 26 2021

Keywords

Comments

The corresponding record values are 1, 3, 4, 6, 7, 10, 14, 15, 17, 20, 22, 24, ... (see the link for more values).

Links

Crossrefs

Cf. A160097.
Subsequence of A025487.
Similar sequences: A002182, A002110 (unitary), A037992 (infinitary), A293185, A306736, A307845, A309141, A318278, A322484, A335386.

Programs

  • Mathematica
    f1[p_, e_] := e + 1; f2[p_, e_] := DivisorSigma[0, e]; ned[1] = 1; ned[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) - Times @@ f2 @@@ f; dm = -1; s = {}; Do[If[(d = ned[n]) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s

A349178 Nonexponential harmonic numbers: numbers k that are not prime powers such that the harmonic mean of the nonexponential divisors of k is an integer.

Original entry on oeis.org

1645, 5742, 6336, 8925, 9450, 88473
Offset: 1

Views

Author

Amiram Eldar, Nov 09 2021

Keywords

Comments

The prime powers are excluded since the primes and the squares of primes have a single nonexponential divisor (the number 1).
a(7) > 6.6*10^10, if it exists.

Examples

			1645 is a term since the set of its nonexponential divisors is {1, 5, 7, 35, 47, 235, 329} and the harmonic mean of this set, 5, is an integer.

Crossrefs

Cf. A160097, A160135.
Similar sequences: A001599, A006086, A063947, A286325, A319745, A348964, A349026.

Programs

  • Mathematica
    dQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m]); expDivQ[n_, d_] := Module[{ft = FactorInteger[n]}, And @@ MapThread[dQ, {ft[[;; , 2]], IntegerExponent[d, ft[[;; , 1]]]}]]; neDivs[1] = {0}; neDivs[n_] := Module[{d = Divisors[n]}, Select[d, ! expDivQ[n, #] &]]; Select[Range[10^4], Length[(d = neDivs[#])] > 1 && IntegerQ @ HarmonicMean[d] &]
Showing 1-2 of 2 results.

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

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