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.

A348585 Numbers k such that A113184(k) = A113184(k+1).

Original entry on oeis.org

1, 8, 27, 375, 459, 620, 1652, 2871, 3451, 3956, 8055, 8636, 8907, 9844, 10647, 12104, 19491, 20155, 27089, 27643, 38180, 41547, 48364, 62379, 74875, 79304, 83780, 90692, 115289, 139460, 146828, 233729, 291819, 297987, 324423, 338547, 365660, 377540, 392635, 403575
Offset: 1

Views

Author

Amiram Eldar, Oct 24 2021

Keywords

Comments

Equivalently, numbers k such that A002129(k) = -A002129(k+1).

Examples

			1 is a term since A113184(1) = A113184(2) = 1.
8 is a term since A113184(8) = A113184(9) = 13.

Links

Crossrefs

Cf. A002129, A113184.
Similar sequences: A002961, A206368, A333261.

Programs

  • Mathematica
    f[p_, e_] := If[p == 2, 2^(e + 1)-3, (p^(e + 1) - 1)/(p - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], s[#] == s[# + 1] &]
f[n_]:=Module[{dn=Divisors[n],odn,edn},odn=Select[dn,OddQ];edn=Select[dn,EvenQ];Abs[Total[odn]-Total[edn]]]; SequencePosition[f/@Range[404000],{x_,x_}][[;;,1]] (* Harvey P. Dale, Apr 28 2025 *)
  • PARI
    f(n) = -sumdiv(n, d, (-1)^d*d); \\ A002129
isok(k) = f(k) + f(k+1) == 0; \\ Michel Marcus, Oct 24 2021

A348586 Numbers k such that abs(A328258(k)) = abs(A328258(k+1)).

Original entry on oeis.org

1, 11, 40, 179, 695, 928, 991, 1079, 2772, 2799, 2839, 6687, 7632, 7739, 7960, 8568, 9347, 10703, 11008, 11472, 12847, 12935, 13580, 14064, 16000, 16260, 17135, 20944, 26432, 27999, 35399, 37236, 42251, 42756, 44199, 55308, 56419, 68976, 70127, 74671, 77748, 83099
Offset: 1

Views

Author

Amiram Eldar, Oct 24 2021

Keywords

Comments

Equivalently, numbers k such that A328258(k) = -A328258(k+1).

Examples

			1 is a term since abs(A328258(1)) = abs(A328258(2)) = 1.
11 is a term since abs(A328258(11)) = abs(A328258(12)) = 12.

Links

Crossrefs

The unitary version of A348585.
Cf. A328258.
Similar sequences: A002961, A064125, A206368, A333261.

Programs

  • Mathematica
    f[p_, e_] := 1 - (-1)^p*(p^e); s[1] = 1; s[n_] := Abs[Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^5], s[#] == s[# + 1] &]
  • PARI
    f(n) = sumdiv(n, d, if (gcd(d, n/d) == 1, (-1)^(d + 1) * d)); \\ A328258
isok(k) = f(k) + f(k+1) == 0; \\ Michel Marcus, Oct 24 2021

A370682 Numbers k such that A370681(k) = A370681(k+1).

Original entry on oeis.org

1, 5, 11, 19, 71, 203, 271, 979, 991, 2755, 5976, 6407, 7004, 8560, 9143, 33552, 46583, 75856, 87955, 90287, 101955, 243271, 265587, 269648, 457135, 510192, 512783, 551172, 559656, 1804555, 1917639, 2902175, 4339952, 6783820, 9842748, 10463980, 17428447, 21677503
Offset: 1

Views

Author

Amiram Eldar, Feb 26 2024

Keywords

Examples

			5 is a term since A370681(5) = A370681(6) = 4.

Links

Crossrefs

Cf. A064125, A333261, A370681.

Programs

  • Mathematica
    s[n_] := Module[{d = Reverse[Select[Divisors[n], CoprimeQ[#, n/#] &]]}, Total[(-1)^(Range[Length[d]] + 1)*d]]; Select[Range[10^5], s[#] == s[# + 1] &]
  • PARI
    s(n) = {my(d = Vecrev(select(x->(gcd(x, n/x) == 1), divisors(n)))); sum(i=1, #d, (-1)^(i+1)*d[i]);}
lista(nmax) = {my(s1 = s(1), s2); for(n = 2, nmax, s2 = s(n); if(s1 == s2, print1(n-1,", ")); s1=s2);}
Showing 1-3 of 3 results.

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