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.

A086288 Number of distinct prime factors of 7-smooth numbers.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A001221, A002473, A086289, A086290.

Programs

  • Mathematica
    PrimeNu[Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &]] (* G. C. Greubel, May 09 2017 *)

Formula

a(n) = A001221(A002473(n)).
a(n) <= 4.

A086290 Minimal exponent in prime factorization of 7-smooth numbers.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A002473, A051904, A086289, A086291.

Programs

  • Mathematica
    minExp[1] = 0; minExp[n_] := Min @@ Last /@ FactorInteger[n]; minExp/@Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &] (* Amiram Eldar, Jan 06 2020 *)

Formula

a(n) = A051904(A002473(n)).
a(n) <= A086291(n) <= A086289(n).

A086291 Maximal exponent in prime factorization of 7-smooth numbers.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A002473, A051903, A086289, A086290.

Programs

  • Mathematica
    maxExp[1] = 0; maxExp[n_] := Max @@ Last /@ FactorInteger[n]; maxExp/@Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &] (* Amiram Eldar, Jan 06 2020 *)

Formula

a(n) = A051903(A002473(n)).
A086290(n) <= a(n) <= A086289(n).

A086295 Sum of all prime factors of 7-smooth numbers.

Original entry on oeis.org

0, 2, 3, 4, 5, 5, 7, 6, 6, 7, 7, 9, 8, 8, 8, 9, 10, 9, 10, 9, 11, 10, 10, 12, 10, 11, 12, 11, 11, 14, 12, 11, 13, 12, 13, 12, 14, 12, 13, 13, 12, 14, 13, 13, 16, 14, 15, 13, 15, 14, 15, 15, 14, 14, 16, 14, 17, 15, 15, 14, 16, 17, 15, 16, 15, 18, 16, 17, 15, 17, 16, 16
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A002473, A001414, A086289, A086293, A086294.

Programs

  • Mathematica
    sumPrimes[1] = 0; sumPrimes[n_] := Plus @@ Times @@@ FactorInteger[n]; sumPrimes/@Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &] (* Amiram Eldar, Jan 06 2020 *)

Formula

a(n) = A001414(A002473(n)).
Showing 1-4 of 4 results.

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