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.

A086289 Total number of prime factors of 7-smooth numbers.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A001222, A002473, A086288, A086290, A086291.

Programs

  • Mathematica
    PrimeOmega[Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &]] (* Amiram Eldar, Jan 06 2020 after G. C. Greubel at A086288 *)

Formula

a(n) = A001222(A002473(n)).
A086290(n) <= A086291(n) <= a(n).

A086293 Sum of divisors of 7-smooth numbers.

Original entry on oeis.org

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 28, 24, 24, 31, 39, 42, 32, 60, 31, 40, 56, 72, 63, 48, 91, 90, 96, 78, 124, 57, 93, 120, 120, 168, 104, 127, 144, 195, 124, 186, 121, 224, 234, 252, 171, 217, 192, 280, 248, 360, 156, 312, 255, 240, 336, 403, 228, 372, 378
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A000203, A002473, A086292.

Programs

  • Mathematica
    DivisorSigma[1, Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &]] (* Amiram Eldar, Jan 06 2020 after G. C. Greubel at A086288 *)

Formula

a(n) = A000203(A002473(n)).

A086292 Number of divisors of 7-smooth numbers.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 6, 4, 4, 5, 6, 6, 4, 8, 3, 4, 6, 8, 6, 4, 9, 8, 8, 6, 10, 3, 6, 8, 8, 12, 6, 7, 8, 12, 6, 10, 5, 12, 12, 12, 6, 9, 8, 12, 10, 16, 4, 12, 8, 8, 12, 15, 6, 12, 12, 10, 16, 6, 18, 8, 14, 9, 12, 16, 16, 12, 9, 20, 6, 6, 8, 18, 9, 16, 16, 18, 12, 18, 12, 14
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A000005, A002473, A086293.

Programs

  • Mathematica
    DivisorSigma[0, Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &]] (* Amiram Eldar, Jan 06 2020 after G. C. Greubel at A086288 *)

Formula

a(n) = A000005(A002473(n)).

A086294 Sum of distinct prime factors of 7-smooth numbers.

Original entry on oeis.org

0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 5, 9, 8, 2, 5, 7, 10, 5, 5, 3, 9, 10, 2, 12, 5, 7, 12, 8, 5, 7, 7, 5, 9, 10, 10, 2, 14, 5, 8, 7, 3, 12, 10, 5, 9, 7, 15, 5, 9, 10, 5, 12, 2, 8, 14, 5, 10, 10, 7, 5, 12, 12, 10, 10, 5, 9, 7, 17, 5, 9, 8, 10, 3, 12, 7, 12, 2, 10, 14, 5, 12, 10, 15, 7, 5, 12, 7
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

Links

Crossrefs

Cf. A002473, A008472, A086288, A086293, A086295.

Programs

  • Mathematica
    sumPrimes[1] = 0; sumPrimes[n_] := Plus @@ First[Transpose[FactorInteger[n]]]; sumPrimes/@Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &] (* Amiram Eldar, Jan 06 2020 *)
dpf7[n_]:=Module[{fi=FactorInteger[n][[All,1]]},If[Max[fi]<11,Total[ fi],Nothing]]; Join[{0},Array[dpf7,400,2]] (* Harvey P. Dale, Feb 26 2022 *)

Formula

a(n) = A008472(A002473(n)).
Showing 1-4 of 4 results.

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

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