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.

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A167305 Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.

Original entry on oeis.org

1, 16, 20, 256, 28, 320, 36, 4096, 400, 448, 52, 5120, 60, 576, 560, 65536, 76, 6400, 84, 7168, 720, 832, 100, 81920, 784, 960, 8000, 9216, 124, 8960, 132, 1048576, 1040, 1216, 1008, 102400, 156, 1344, 1200, 114688, 172, 11520, 180, 13312, 11200, 1600
Offset: 1

Views

Author

Jaroslav Krizek, Nov 01 2009

Keywords

Links

Crossrefs

Cf. A001222, A165825, A166590.

Programs

  • Mathematica
    a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (4*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Formula

Multiplicative with a(p^e) = (4*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+2))^e(k).
a(n) = A165825(n) * A166590(n) = 4^bigomega(n) * A166590(n) = 4^A001222(n) * A166590(n).

A167314 Totally multiplicative sequence with a(p) = 4*(p-3) for prime p.

Original entry on oeis.org

1, -4, 0, 16, 8, 0, 16, -64, 0, -32, 32, 0, 40, -64, 0, 256, 56, 0, 64, 128, 0, -128, 80, 0, 64, -160, 0, 256, 104, 0, 112, -1024, 0, -224, 128, 0, 136, -256, 0, -512, 152, 0, 160, 512, 0, -320, 176, 0, 256, -256, 0, 640, 200, 0, 256, -1024, 0, -416, 224, 0, 232
Offset: 1

Views

Author

Jaroslav Krizek, Nov 01 2009

Keywords

Links

Crossrefs

Cf. A001222, A165825, A166589.

Programs

  • Mathematica
    a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)
f[p_, e_] := (4*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Formula

Multiplicative with a(p^e) = (4*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-3))^e(k).
a(3k) = 0 for k >= 1.
a(n) = A165825(n) * A166589(n) = 4^bigomega(n) * A166589(n) = 4^A001222(n) * A166589(n).

A167323 Totally multiplicative sequence with a(p) = 4*(p+3) for prime p.

Original entry on oeis.org

1, 20, 24, 400, 32, 480, 40, 8000, 576, 640, 56, 9600, 64, 800, 768, 160000, 80, 11520, 88, 12800, 960, 1120, 104, 192000, 1024, 1280, 13824, 16000, 128, 15360, 136, 3200000, 1344, 1600, 1280, 230400, 160, 1760, 1536, 256000, 176, 19200, 184, 22400
Offset: 1

Views

Author

Jaroslav Krizek, Nov 01 2009

Keywords

Links

Crossrefs

Cf. A001222, A165825, A166591.

Programs

  • Mathematica
    a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (4*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)

Formula

Multiplicative with a(p^e) = (4*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+3))^e(k).
a(n) = A165825(n) * A166591(n) = 4^bigomega(n) * A166591(n) = 4^A001222(n) * A166591(n).
Previous Showing 11-13 of 13 results.

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