A113458 Least k such that k, k+n and k+2n have the same prime signature.

33, 3, 155, 3, 77, 5, 51, 3, 77, 3, 35, 5, 50, 3, 187, 6, 21, 5, 39, 3, 145, 33, 39, 5, 69, 39, 91, 3, 33, 7, 15, 12, 221, 3, 28, 7, 21, 3, 55, 3, 33, 5, 91, 66, 209, 69, 35, 5, 50, 3, 115, 39, 141, 5, 51, 6, 145, 85, 15, 7, 21, 93, 95, 3, 57, 5, 51, 3, 65, 15, 35, 7, 69, 55, 287, 6

Offset: 1

Author

David Wasserman, Jan 08 2006

Keywords

• easy
• nonn

Comments

Third row of A113456.

Examples

			a(4) = 3 because 3, 7 and 11 have the same prime signature.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A052214, A113456, A113467.

Programs

Maple

s:= n-> sort(map(i-> i[2], ifactors(n)[2])):
a:= proc(n) option remember; local k; for k
      while s(k)<>s(k+n) or s(k)<>s(k+2*n) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 28 2018

Mathematica

s[n_] := FactorInteger[n][[All, 2]] // Sort;
a[n_] := Module[{k}, For[k = 2, True, k++, If[s[k] == s[k+n] == s[k+2n], Return[k]]]];
Array[a, 100] (* Jean-François Alcover, Nov 05 2020 *)