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.

A349467 Numbers k such that A349410(k) = 1.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 17, 19, 21, 23, 25, 28, 29, 31, 32, 33, 36, 37, 39, 40, 41, 43, 47, 48, 49, 51, 53, 57, 59, 61, 67, 69, 70, 71, 73, 75, 79, 81, 83, 87, 89, 90, 93, 96, 97, 98, 101, 103, 107, 109, 110, 111, 113, 120, 121, 123, 126, 127, 128, 129, 130
Offset: 1

Views

Author

Tejo Vrush, Nov 18 2021

Keywords

Comments

Does this sequence have density 1/3? This sequence has infinitely many terms because every prime number is a term.
The numbers of terms not exceeding 10^k for k = 1, 2, ... are 8, 50, 396, 3566, 33943, 332042, 3297317, 32983277, ... Apparently this sequence has an asymptotic density of about 0.33. - Amiram Eldar, Nov 18 2021

Crossrefs

Cf. A349410.

Programs

  • Mathematica
    a[n_] := Module[{s = NestWhileList[n*DivisorSigma[0, #] &, 1, UnsameQ, All]}, Differences[Position[s, s[[-1]]]][[1, 1]]]; Select[Range[130], a[#] == 1 &] (* Amiram Eldar, Nov 18 2021 *)

A349428 Smallest k such that A349410(k) = n or -1 if no such number exists.

Original entry on oeis.org

1, 4, 15, 30, 42, 360, 196, 525, 2080, 320, 7168, 123200, 35200, 150920, 196000, 1232000, 61236, 466560, 106831872, 49787136, 14580000, 155648000, 94058496, 123561984, 47385000
Offset: 1

Views

Author

Tejo Vrush, Nov 17 2021

Keywords

Crossrefs

Cf. A349410.
Similar sequences: A005179, A348184.

Programs

  • Mathematica
    f[n_] := Module[{s = NestWhileList[n * DivisorSigma[0, #] &, 1, UnsameQ, All]}, Differences[Position[s, s[[-1]]]][[1, 1]]]; seq[len_, nmax_] := Module[{v = Table[0, {len}], n = 1, c = 0, i}, While[c < len && n < nmax, i = f[n]; If[i <= len && v[[i]] == 0, c++; v[[i]] = n]; n++]; TakeWhile[v, # > 0 &]]; seq[15, 10^6] (* Amiram Eldar, Nov 17 2021 *)

Extensions

Escape clause value changed to -1. - N. J. A. Sloane, Jan 14 2022

A349483 Length of cycle reached when iterating the mapping x-> n*A035116(x) on 1.

Original entry on oeis.org

1, 2, 2, 2, 4, 2, 5, 2, 2, 7, 2, 1, 2, 5, 6, 1, 2, 2, 2, 3, 2, 2, 2, 1, 1, 2, 4, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 2, 1, 3, 2, 4, 2, 1, 3, 2, 2, 4, 3, 6, 1, 1, 2, 2, 3, 3, 1, 2, 2, 4, 2, 2, 1, 3, 3, 3, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 3, 2, 8, 1, 2, 2, 3, 3, 2, 1, 3, 2, 3, 1, 1, 1, 2, 3, 1, 2, 4, 1, 2
Offset: 1

Views

Author

Tejo Vrush, Nov 19 2021

Keywords

Comments

The terms 1-25 all appear below 10^8; the last of these are a(12545280) = 21, a(12684672) = 24, and a(96940800) = 25. - Charles R Greathouse IV, Nov 23 2021

Examples

			For n = 2, 1 --> 2 --> 8 --> 32 --> 72 --> 288 --> 648 --> 800 --> 648. The cycle reached has just two terms: 648 and 800. Therefore, a(2) = 2.

Links

Crossrefs

Cf. A035116.
Similar sequences: A349410.

Programs

  • Mathematica
    a[n_] := Module[{s = NestWhileList[n*DivisorSigma[0, #]^2 &, 1, UnsameQ, All]}, Differences[Position[s, s[[-1]]]][[1, 1]]]; Array[a, 100] (* Amiram Eldar, Nov 19 2021 *)
  • PARI
    brent(f,x)=my(pow=1,lam=1,tortoise=x,hare=f(x)); while(tortoise!=hare, if(pow==lam, tortoise=hare; pow<<=1; lam=0); hare=f(hare); lam++); lam
a(n)=brent(k->n*numdiv(k)^2,1) \\ Charles R Greathouse IV, Nov 19 2021
Showing 1-3 of 3 results.

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

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