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.

A073814 a(n) is the smallest number k such that A073813(k) = prime(n).

Original entry on oeis.org

2, 4, 15, 33, 90, 129, 227, 288, 429, 694, 798, 1149, 1417, 1565, 1879, 2399, 2993, 3201, 3879, 4365, 4623, 5429, 6002, 6920, 8245, 8948, 9314, 10067, 10457, 11245, 14251, 15184, 16627, 17130, 19711, 20253, 21919, 23653, 24845, 26687, 28604, 29248, 32612, 33303, 34719, 35436, 39893, 44622, 46254
Offset: 1

Views

Author

Labos Elemer, Aug 15 2002

Keywords

Examples

			a(6)=129 means that c[129]-Max[URS[c[129]]=Prime[6]: c[129]=169, Max[URS[169]]=Max{26,39,...,143,156}=156; difference=169-156=13=6th prime. Suspicion: A073813(n) is always prime number!

Crossrefs

Cf. A045763, A073759, A002808, A073813.
Cf. A120389. [From R. J. Mathar, Aug 07 2008]

Programs

  • Mathematica
    c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x]; tn[x_] := Table[j, {j, 1, x}]; di[x_] := Divisors[x]; rrs[x_] := Flatten[Position[GCD[tn[x], x], 1]]; rs[x_] := Union[rrs[x], di[x]]; urs[x_] := Complement[tn[x], rs[x]]; Do[s=c[n]-Max[urs[c[n]]]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10}]; t
nn = 6 * 10^4; s = Function[k, k - SelectFirst[Range[k - 2, 2, -1], 1 < GCD[#, k] < # &]] /@ Select[Range[6, nn], ! PrimeQ@ # &]; Table[SelectFirst[Range@ Length@ s, s[[# - 1]] == Prime@ n &], {n, 49}] (* Michael De Vlieger, Mar 28 2016, Version 10 *)

Formula

Min{x; c[x]-Max[URS[c[x]]]=p(n)}, p(n)=n-th prime. See program.

Extensions

Definition corrected by Gionata Neri, Mar 28 2016
More terms from Michael De Vlieger, Mar 28 2016

A073806 Number of divisors of sum of square of divisors.

Original entry on oeis.org

1, 2, 4, 4, 4, 6, 6, 4, 4, 8, 4, 16, 8, 8, 12, 4, 8, 8, 4, 16, 12, 8, 8, 12, 8, 12, 12, 24, 4, 18, 8, 16, 12, 12, 18, 12, 8, 8, 18, 16, 6, 15, 12, 16, 12, 12, 16, 16, 8, 16, 18, 32, 8, 18, 12, 16, 12, 8, 4, 48, 4, 16, 24, 4, 24, 18, 8, 32, 18, 24, 4, 16, 16, 12, 32, 16, 18, 24, 4, 16, 6
Offset: 1

Views

Author

Labos Elemer, Aug 13 2002

Keywords

Examples

			n = 10: D = {1,2,5,10}, sigma(2,10) = 1 + 4 + 25 + 100 = 130, D(130) = {1,2,5,10,13,26,65,130}, so a(10) = 8.

Links

Crossrefs

Cf. A000005, A000203, A001157, A062068, A073802-A073813.

Programs

  • Mathematica
    a[n_] := DivisorSigma[0, DivisorSigma[2, n]]; Array[a, 81] (* Amiram Eldar, Aug 01 2019 *)

Formula

a(n) = A000005(A001157(n)) = d(sigma(2, n)).

A073807 Number of divisors of sum of cube of divisors.

Original entry on oeis.org

1, 3, 6, 2, 12, 18, 8, 12, 2, 20, 18, 12, 8, 24, 36, 4, 32, 6, 24, 24, 24, 30, 36, 72, 4, 24, 32, 16, 24, 60, 36, 16, 60, 48, 60, 4, 16, 72, 24, 80, 24, 72, 24, 36, 24, 60, 60, 24, 8, 12, 96, 16, 20, 96, 80, 96, 50, 40, 72, 72, 16, 108, 16, 8, 54, 100, 12, 64, 108, 100, 32, 24
Offset: 1

Views

Author

Labos Elemer, Aug 13 2002

Keywords

Comments

a(n) = 2 for n in A063783. - Robert Israel, Jul 12 2023

Examples

			For n=10: D={1,2,5,10}, 1+8+125+1000=1134, divisors(1134)={1,2,3,6,7,9,14,18,21,27,42,54,63,81,126,162,189,378,567,1134} so a(10)=20.

Links

Crossrefs

Cf. A000005, A001158, A062068, A063783, A073802-A073813.

Programs

  • Maple
    f:= n -> numtheory:-tau(numtheory:-sigma[3](n)):
map(f, [$1..100]); # Robert Israel, Jul 12 2023
  • Mathematica
    Table[DivisorSigma[0,DivisorSigma[3,n]],{n,80}] (* Harvey P. Dale, Dec 13 2011 *)
  • PARI
    a(n) = numdiv(sigma(n, 3)); \\ Michel Marcus, Jul 13 2023

Formula

a(n) = A000005(A001158(n)).
Showing 1-3 of 3 results.

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