A113467 -id:A113467 - cp's OEIS frontend

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

David Wasserman, Jan 08 2006

Third row of A113456.

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

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

Cf. A052214, A113456, A113467.

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

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 *)

A113465 Rectangular array read by antidiagonals: a(n, d) is the smallest number that starts an arithmetic progression with common difference d of n numbers with the same number of divisors.

Original entry on oeis.org

1, 2, 1, 33, 3, 1, 242, 3, 2, 1, 11605, 213, 119, 3, 1, 28374, 213, 3445, 3, 2, 1, 171893, 1383, 15026, 111, 77, 5, 1, 1043710445721, 3091, 74783, 201, 8718, 5, 8, 1

Offset: 1

David Wasserman, Jan 08 2006

First two columns are A006558 and A113466. First four rows are A000012, A065559, A113467 and A113468. a(9, 1) is unknown; the rest of the 9th antidiagonal is 8129,88015,201,8718,5,8,3,1.

			a(4, 3) = 3445 because 3445, 3448, 3451 and 3454 each have 8 divisors.

Cf. A006558, A065559, A113456, A113466, A113467, A113468.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica