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.

A346389 a(n) is the number of proper divisors of A324297(n) ending with 6.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Jul 15 2021

Keywords

Examples

			a(12) = 4 since there are 4 proper divisors of A324297(12) = 576 ending with 6: 6, 16, 36 and 96.
		

Crossrefs

Cf. A017341, A032741, A324297, A324298, A337856, A346388 (ending with 5), A346392.

Programs

  • Mathematica
    b={}; For[n=0, n<=450, n++, For[k=0, k<=n, k++, If[Mod[10*n+6, 10*k+6]==0 && Mod[(10*n+6)/(10*k+6), 10]==6 && 10*n+6>Max[b], AppendTo[b, 10*n+6]]]]; (* A324297 *) a={}; For[i =1, i<=Length[b], i++, AppendTo[a, Length[Drop[Select[Divisors[Part[b, i]], (Mod[#,10]==6&)], -1]]]]; a

Formula

a(n) = A346392(A324297(n)).

A346388 a(n) is the number of proper divisors of A053742(n) ending with 5.

Original entry on oeis.org

1, 3, 2, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 7, 3, 3, 7, 5, 3, 7, 3, 3, 8, 3, 5, 7, 3, 5, 7, 3, 3, 11, 5, 3, 7, 3, 3, 7, 7, 3, 9, 3, 5, 7, 3, 7, 7, 5, 3, 11, 3, 3, 11, 3, 3, 7, 3, 5, 11, 7, 5, 7, 4, 3, 7, 3, 7, 11, 3, 3, 7, 7, 5, 11, 3, 3, 11, 5, 3, 7, 7, 3, 11, 3, 5
Offset: 0

Views

Author

Stefano Spezia, Jul 15 2021

Keywords

Examples

			a(10) = 7 since there are 7 proper divisors of A053742(10) = 525 ending with 5: 5, 15, 25, 35, 75, 105 and 175.
		

Crossrefs

Cf. A032741, A053742, A346389 (ending with 6), A346392.

Programs

  • Mathematica
    a[n_]:=Length[Drop[Select[Divisors[25+50n], (Mod[#,10]==5&)], -1]]; Array[a, 90, 0]

Formula

a(n) = A346392(A053742(n)).

A346510 a(n) is the number of nontrivial divisors of A346507(n) ending with 1.

Original entry on oeis.org

1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 4, 2
Offset: 1

Views

Author

Stefano Spezia, Jul 21 2021

Keywords

Examples

			a(42) = 4 since there are 4 nontrivial divisors of A346507(42) = 2541 ending with 1: 11, 21, 121 and 231.
		

Crossrefs

Cf. A017281, A070824, A346388 (ending with 5), A346389 (ending with 6), A346392, A346507, A346508, A346509.

Programs

  • Mathematica
    b={}; For[n=1, n<=500, n++, For[k=1, kMax[b], AppendTo[b, 10n+1]]]]; (* A346507 *) a={}; For[i =1, i<=Length[b], i++, AppendTo[a, Length[Drop[Select[Divisors[Part[b, i]], (Mod[#, 10]==1&)], -1]]-1]]; a
  • PARI
    f(n) = sumdiv(n, d, (d>1) && (d(f(x)), [1..5000])) \\ Michel Marcus, Jul 28 2021
    
  • Python
    from sympy import divisors
    def f(n): return sum(d%10 == 1 for d in divisors(n)[1:-1])
    def A346507upto(lim): return sorted(set(a*b for a in range(11, lim//11+1, 10) for b in range(a, lim//a+1, 10)))
    print(list(map(f, A346507upto(5000)))) # Michael S. Branicky, Jul 31 2021

Formula

a(n) = A346392(A346507(n)) - 1.
Showing 1-3 of 3 results.