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 1-4 of 4 results.

A112759 Total number of prime factors of n-th 5-smooth number.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 2, 4, 3, 3, 4, 2, 3, 3, 5, 4, 4, 3, 5, 3, 4, 4, 6, 5, 3, 5, 4, 4, 6, 4, 5, 5, 3, 7, 4, 6, 4, 6, 5, 5, 7, 5, 6, 4, 6, 5, 4, 8, 5, 7, 5, 7, 6, 6, 4, 8, 6, 5, 7, 5, 7, 6, 5, 9, 6, 8, 6, 4, 8, 7, 5, 7, 6, 5, 9, 7, 6, 8, 6, 8, 7, 6, 10, 7, 5, 9, 7, 6, 5, 9, 8, 6, 8, 7, 6, 10, 8, 7, 9, 7
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 18 2005

Keywords

Links

Crossrefs

Cf. A001222, A051037, A069352, A112754, A112758, A112760, A112761, A112762.

Programs

  • Mathematica
    PrimeOmega @ Select[Range[3000], Last @ Map[First, FactorInteger[#]] <= 5 &] (* Amiram Eldar, Feb 07 2020 *)

Formula

a(n) = A001222(A051037(n));
a(n) = A112760(n) + A112761(n) + A112762(n).

A112762 Exponent of 5 (value of k) in n-th number of the form 2^i*3^j*5^k.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 2, 1, 0, 1, 0, 2, 0, 1, 3, 0, 1, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 0, 3, 0, 1, 0, 2, 1, 0, 1, 3, 0, 2, 1, 0, 2, 1, 0, 3, 0, 1, 0, 2, 4, 1, 0, 2, 1, 0, 3, 0, 2, 1, 0, 2, 1, 0, 3, 0, 1, 3, 0, 2, 1, 4, 1, 0, 2, 1, 0, 3, 0, 2, 1, 0, 2, 4
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 18 2005

Keywords

Links

Crossrefs

Cf. A022337, A051037, A112765, A112760, A112761.

Programs

  • Mathematica
    IntegerExponent[#, 5] & /@ Select[Range[3000], Last @ Map[First, FactorInteger[#]] <= 5 &] (* Amiram Eldar, Feb 07 2020 *)

Formula

a(n) = A112765(A051037(n));
a(n) = A112759(n) - A112760(n) - A112761(n).

A112761 Exponent of 3 (value of j) in n-th number of the form 2^i*3^j*5^k.

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 0, 3, 1, 0, 2, 0, 2, 1, 0, 3, 1, 0, 2, 1, 0, 4, 2, 1, 0, 3, 1, 0, 0, 3, 2, 1, 0, 4, 2, 1, 0, 3, 2, 1, 5, 0, 0, 3, 2, 1, 0, 4, 2, 1, 1, 0, 4, 3, 2, 1, 5, 0, 0, 3, 2, 1, 0, 0, 4, 3, 2, 6, 1, 1, 0, 4, 3, 2, 1, 5, 0, 0, 3, 2, 2, 1, 5, 0, 0, 4, 3, 2, 6, 1, 1, 0, 4, 3, 2, 1
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 18 2005

Keywords

Links

Crossrefs

Cf. A007949, A022336, A022329, A051037, A112759, A112760, A112762.

Programs

  • Mathematica
    IntegerExponent[#, 3] & /@ Select[Range[3000], Last @ Map[First, FactorInteger[#]] <= 5 &] (* Amiram Eldar, Feb 07 2020 *)

Formula

a(n) = A007949(A051037(n));
a(n) = A112759(n) - A112760(n) - A112762(n).

A112758 Number of distinct prime factors of n-th 5-smooth number.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 3, 1, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 2, 2, 3, 1, 1, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 1, 2, 1, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 1, 3, 2, 3, 1, 2, 2, 2, 3, 1, 3, 2, 2, 3, 2, 3, 3, 2, 2, 1, 3, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 18 2005

Keywords

Links

Crossrefs

Cf. A001221, A051037, A086412, A112753, A112759, A112760, A112761, A112762.

Programs

  • Mathematica
    aa = {}; Do[If[8 n - EulerPhi[30 n] == 0, AppendTo[aa, n]], {n, 1, 100}]; PrimeNu[aa]  (* G. C. Greubel, May 07 2017 *)
PrimeNu[#]&/@Select[Range[2000],Max[FactorInteger[#][[All,1]]]<6&] (* Harvey P. Dale, Apr 12 2020 *)

Formula

a(n) = A001221(A051037(n)).
a(n) = 3 - 0^A112760(n) - 0^A112761(n) - 0^A112762(n).
a(n) <= 3.
Showing 1-4 of 4 results.

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