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.

A333262 Number of steps to reach 1 by iterating the alternating sum of divisors function A071324 starting from n.

Original entry on oeis.org

0, 1, 2, 3, 4, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 8, 9, 7, 8, 7, 8, 8, 9, 7, 8, 9, 10, 8, 9, 9, 9, 9, 10, 10, 11, 8, 10, 9, 10, 10, 11, 9, 11, 9, 10, 10, 12, 10, 11, 11, 12, 10, 11, 9, 10, 9, 10, 10, 11, 10, 10, 12, 10, 11, 12, 11, 11, 11, 12, 13, 14, 9, 11, 11
Offset: 1

Views

Author

Amiram Eldar, Mar 13 2020

Keywords

Examples

			a(3) = 2 since it takes 2 iterations of A071324 to reach from 3 to 1: 3 -> 2 -> 1.

Links

Crossrefs

Cf. A071324, A330786.

Programs

  • Mathematica
    f[n_] := Plus @@ (-(d = Divisors[n])*(-1)^(Range[Length[d],1,-1])); a[n_] := Length @ FixedPointList[f,n] - 2; Array[a, 100]

Formula

a(n) = 0 if n = 1 and a(n) = a(A071324(n)) + 1 otherwise.

A331017 Numbers that equal to the sum of their iterated absolute alternating sum-of-divisors function (A206369).

Original entry on oeis.org

3, 10, 21, 63, 104, 152, 170, 358, 567, 651, 3826, 4664, 5583, 5943, 39248, 943228, 1906503, 9166540, 35702868, 701792828, 825415941, 2275142000, 5805372939
Offset: 1

Views

Author

Amiram Eldar, Jan 06 2020

Keywords

Examples

			10 is a term since the iterations of A206369 with a starting value of 10 give A206369(10) = 4, A206369(4) = 3, A206369(3) = 2, and A206369(2) = 1, whose sum is 4 + 3 + 2 + 1 = 10.

Crossrefs

Cf. A082897, A206369, A330786 (number of iterations).

Programs

  • Mathematica
    f[p_, e_] := Sum[(-1)^(e - k)*p^k, {k, 0, e}]; s[1] = 1; s[n_] := s[n] = Times @@ (f @@@ FactorInteger[n]); Select[Range[1000], Plus @@ FixedPointList[s, #] == 2 # + 1 &]

A333264 Least number k that reaches 1 after n iterations of A206369.

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 15, 17, 69, 121, 137, 467, 985, 1949, 4049, 8117, 14641, 36383, 62501, 125003, 250007, 958081, 1817513, 3325981, 8062091, 21233813, 42467627, 125828819, 343955189
Offset: 0

Views

Author

Amiram Eldar, Mar 13 2020

Keywords

Comments

Least number k such that A330786(k) = n.

Examples

			a(5) = 8 since 8 is the least number that reaches 1 after 5 iterations of A206369: 8 -> 5 -> 4 -> 3 -> 2 -> 1.

Crossrefs

Cf. A206369, A330786.

Programs

  • Mathematica
    f[p_, e_] := Sum[(-1)^(e-k)*p^k, {k, 0, e}]; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); numiter[n_] := Length @ FixedPointList[s, n] - 2; n = 0; seq={}; Do[If[numiter[k] == n, AppendTo[seq, k]; n++], {k, 1, 1000}]; seq
Showing 1-3 of 3 results.

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

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