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.

A225004 a(n) is the largest multiple of n with fewer than twice as many divisors as n.

Original entry on oeis.org

1, 4, 9, 16, 25, 18, 49, 64, 81, 50, 121, 48, 169, 98, 75, 256, 289, 162, 361, 100, 147, 242, 529, 192, 625, 338, 729, 196, 841, 150, 961, 1024, 363, 578, 245, 324, 1369, 722, 507, 400, 1681, 294, 1849, 484, 405, 1058, 2209, 768, 2401, 1250, 867, 676, 2809
Offset: 1

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Author

J. Lowell, Apr 23 2013

Keywords

Comments

Conjecture: a(n) is always a divisor of n^2.

Examples

			a(6) = 18 because 6 has 4 divisors and term must have fewer than 8 divisors. Only 6, 12, and 18 are multiples of 6 with fewer than 8 divisors.
		

Crossrefs

Cf. A000005.

Programs

  • Mathematica
    a[n_] := If[n == 1, 1, Block[{nd, p, e, r, mu=0}, {p, e} = Transpose@ FactorInteger@ n; nd = 2*Times @@ (1+e); r[w_, i_] := Block[{v = w}, If[i < 1, mu = Max[mu, Times @@ (p^w)], While[Times @@ (1 + v) < nd, r[v, i-1]; v[[i]]++]]]; r[e, Length@e]; mu]]; Array[a, 46] (* Giovanni Resta, Apr 28 2013 *)

Extensions

Some terms corrected by Giovanni Resta, Apr 28 2013