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.

Showing 1-3 of 3 results.

A332037 Indices of records in A332036.

Original entry on oeis.org

1, 12, 24, 60, 120, 240, 360, 720, 1440, 2160, 2880, 4320, 5760, 7200, 8640, 12960, 14400, 17280, 21600, 25920, 28800, 30240, 34560, 40320, 43200, 51840, 60480, 86400, 120960, 172800, 181440, 241920, 259200, 302400, 362880, 483840, 518400, 604800, 725760, 907200
Offset: 1

Views

Author

Amiram Eldar, Feb 05 2020

Keywords

Comments

Numbers k such that bsigma(x) = k has more solutions x than any smaller k, where bsigma(x) is the sum of bi-unitary divisors of x (A188999).
The bi-unitary version of A145899.
The corresponding number of solutions for each term is 1, 2, 3, 5, 7, 12, 13, 20, ... (see the link for more values).

Examples

			There are 3 solutions to bsigma(x) = 24: bsigma(14) = bsigma(15) = bsigma(23) = 24. For all m < 24 there are 2 or fewer solutions to bsigma(x) = m, thus 24 is in the sequence.

Links

Crossrefs

Cf. A145899, A188999, A289132, A332036, A332037, A332039.

Programs

  • Mathematica
    fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 10000; v = Table[0, {m}]; Do[b = bsigma[k]; If[b <= m, v[[b]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

A332041 Indices of records in A332040.

Original entry on oeis.org

1, 6, 30, 330, 390, 2730, 5460, 12090, 60060, 92820, 223860, 1021020, 1922700, 3805620, 13458900, 41861820, 110362980, 113573460, 227146920, 251170920, 502341840, 563603040, 888287400, 1270629360, 1776574800, 3310889400, 23107724640, 27939071160, 33754921200, 36419783400
Offset: 1

Views

Author

Amiram Eldar, Feb 05 2020

Keywords

Comments

Numbers k such that esigma(x) = k has more solutions x than any smaller k, where esigma(x) is the sum of exponential divisors of x (A051377).
The exponential version of A145899.
The corresponding number of solutions for each term is 1, 2, 5, 6, 8, 9, 10, 12, 15, 16, 19, 22, 27, 29, 35, 37, 38, 44, 45, 47, 50, 51, 52, 53, 66, 80, 83, 89, 95, 102.

Examples

			There are 2 solutions to esigma(x) = 6: esigma(4) = esigma(6) = 6. For all m < 6 there are no more than one solution to esigma(x) = m, thus 6 is in the sequence.

Crossrefs

Cf. A051377, A145899, A289132, A332037, A332039, A332040.

Programs

  • Mathematica
    f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; m = 10000; v = Table[0, {m}]; Do[sig = esigma[k]; If[sig <= m, v[[sig]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

Extensions

a(26)-a(30) from Giovanni Resta, Feb 06 2020

A332043 Indices of records in A332042.

Original entry on oeis.org

1, 6, 12, 24, 48, 72, 144, 288, 576, 864, 1152, 1440, 1728, 2160, 2304, 2880, 4320, 5760, 8640, 17280, 25920, 34560, 51840, 69120, 103680, 120960, 138240, 155520, 181440, 207360, 241920, 311040, 362880, 414720, 483840, 622080, 725760, 967680, 1244160, 1451520
Offset: 1

Views

Author

Amiram Eldar, Feb 05 2020

Keywords

Comments

Numbers k such that psi(x) = k has more solutions x than any smaller k, where psi(x) is the Dedekind psi function (A001615).
The corresponding number of solutions for each term is 1, 2, 4, 5, 6, 9, 11, 17, ... (see the link for more values).

Examples

			There are 2 solutions to psi(x) = 6: psi(4) = psi(5) = 6. For all m < 6 there are no more than one solution to psi(x) = m, thus 6 is in the sequence.

Links

Crossrefs

Cf. A001615, A145899, A289132, A332037, A332039, A332041, A332042.

Programs

  • Mathematica
    psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); m = 10000; v = Table[0, {m}]; Do[i = psi[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s
Showing 1-3 of 3 results.

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

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