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.

A371209 Number of ordered factorizations of n into factors > 2.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 2, 1, 3, 1, 3, 3, 1, 1, 5, 2, 1, 4, 3, 1, 5, 1, 3, 3, 1, 3, 9, 1, 1, 3, 5, 1, 5, 1, 3, 8, 1, 1, 10, 2, 3, 3, 3, 1, 8, 3, 5, 3, 1, 1, 15, 1, 1, 8, 5, 3, 5, 1, 3, 3, 5, 1, 18, 1, 1, 8, 3, 3, 5, 1, 10, 8, 1, 1, 15, 3, 1, 3
Offset: 1

Views

Author

Ilya Gutkovskiy, Mar 15 2024

Keywords

Examples

			a(12) = 3: 12 = 3*4 = 4*3.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 2, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 87}]

Formula

a(1) = 1; a(n) = Sum_{d|n, n/d > 2} a(d).

A371211 Number of ordered factorizations of n into factors > 3.

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Mar 15 2024

Keywords

Examples

			a(20) = 3: 20 = 4*5 = 5*4.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 3, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 89}]
  • PARI
    memoA371211 = Map();
    A371211(n) = if(1==n,1,my(v); if(mapisdefined(memoA371211,n,&v), v, v = sumdiv(n,d,if((n/d)<=3, 0, A371211(d))); mapput(memoA371211,n,v); (v))); \\ Antti Karttunen, Jan 15 2025

Formula

a(1) = 1; a(n) = Sum_{d|n, n/d > 3} a(d).

Extensions

More terms from Antti Karttunen, Jan 15 2025

A371212 Number of ordered factorizations of n into factors > 4.

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Mar 15 2024

Keywords

Examples

			a(30) = 3: 30 = 5*6 = 6*5.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 4, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 92}]
  • PARI
    memoA371212 = Map();
    A371212(n) = if(1==n,1,my(v); if(mapisdefined(memoA371212,n,&v), v, v = sumdiv(n,d,if((n/d)<=4, 0, A371212(d))); mapput(memoA371212,n,v); (v))); \\ Antti Karttunen, Jan 16 2025

Formula

a(1) = 1; a(n) = Sum_{d|n, n/d > 4} a(d).

Extensions

More terms from Antti Karttunen, Jan 16 2025
Showing 1-3 of 3 results.