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.

A348215 a(n) is the sum of the iterated A348158 starting from n until a fixed point is reached.

Original entry on oeis.org

0, 1, 0, 3, 0, 3, 0, 7, 0, 5, 0, 7, 0, 7, 0, 15, 0, 9, 0, 15, 0, 11, 0, 15, 0, 13, 0, 21, 0, 15, 0, 31, 0, 17, 0, 25, 0, 19, 0, 31, 0, 21, 0, 33, 0, 23, 0, 31, 0, 25, 0, 39, 0, 27, 0, 49, 0, 29, 0, 31, 0, 31, 57, 120, 0, 33, 0, 51, 0, 35, 0, 57, 0, 37, 0, 57
Offset: 1

Views

Author

Amiram Eldar, Oct 07 2021

Keywords

Comments

The first odd number k with a(k) > 0 is k = 63.

Examples

			a(4) = 3 since the iterations of the map x -> A348158(x) starting from 4 are 4 -> 3.
a(64) = 120 since the iterations of the map x -> A348158(x) starting from 64 are 64 -> 63 -> 57, and 63 + 57 = 120.

Links

Crossrefs

Cf. A092693, A326835, A348158, A348213, A348214.

Programs

  • Mathematica
    f[n_] := Plus @@ DeleteDuplicates @ Map[EulerPhi, Divisors[n]]; a[n_] := Plus @@ Most @ FixedPointList[f, n] - n; Array[a, 100]

Formula

a(n) = 0 if and only if n is in A326835.
a(2*n) > 0 for all n.

A348216 Numbers k such that A348215(k) = k.

Original entry on oeis.org

120, 1320, 2760, 3480, 3720, 4920, 5160, 5640, 6360, 7080, 7320, 8040, 8520, 8760, 9480, 9960, 10680, 11640, 12120, 12360, 12840, 13080, 13560, 14520, 15240, 15720, 16440, 16680, 17880, 18120, 18840, 19560, 20040, 20760, 21480, 21720, 22920, 23160, 23640, 23880
Offset: 1

Views

Author

Amiram Eldar, Oct 07 2021

Keywords

Comments

Are there odd terms in this sequence? There are none below 10^8.

Examples

			120 is a term since the iterations of the map x -> A348158(x) starting from 120 are 120 -> 63 -> 57 and A348215(120) = 57 + 63 = 120.

Links

Crossrefs

Cf. A082897, A348158, A348213, A348214, A348215.

Programs

  • Mathematica
    f[n_] := Plus @@ DeleteDuplicates @ Map[EulerPhi, Divisors[n]]; s[n_] := Plus @@ Most @ FixedPointList[f, n] - n; Select[Range[24000], s[#] == # &]

A348265 a(n) is the least number k such that A348264(k) = n, or -1 if no such number exists.

Original entry on oeis.org

1, 2, 84, 1596, 410652, 9114300, 10628100, 3012406320
Offset: 0

Views

Author

Amiram Eldar, Oct 09 2021

Keywords

Examples

			n The n iterations of a(n) under the map x -> A348264(x)
- --------------------------------------------------------------------------------
0 1
1 2 -> 1
2 84 -> 78 -> 39
3 1596 -> 1428 -> 1326 -> 663
4 410652 -> 410172 -> 366996 -> 340782 -> 170391
5 9114300 -> 8871252 -> 8680848 -> 8661648 -> 8487018 -> 4243509
6 10628100 -> 10344684 -> 10309980 -> 10287900 -> 10013556 -> 9298302 -> 4649151
7 3012406320 -> 2999958360 -> 2927545572 -> 2917724340 -> 2911475700 -> 2833836348 -> 2631419466 -> 1315709733

Crossrefs

The unitary version of A348214.
Cf. A348004, A348264.

Programs

  • Mathematica
    f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; sum[n_] := Plus @@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; s[n_] := -2 + Length@FixedPointList[sum, n]; seq[m_, lim_] := Module[{t = Table[0, {m}], c = 0, n = 1}, While[c < m && n < lim, i = s[n] + 1; If[i <= m && t[[i]] == 0, c++; t[[i]] = n]; n++]; TakeWhile[t, # > 0 &]]; seq[5, 10^6]
Showing 1-3 of 3 results.

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

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