A224866 Numbers of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).

2, 5, 9, 10, 17, 26, 28, 33, 37, 50, 65, 73, 82, 101, 109, 122, 126, 129, 145, 170, 197, 201, 217, 226, 244, 257, 289, 290, 325, 344, 362, 393, 401, 433, 442, 485, 501, 513, 530, 577, 626, 649, 676, 677, 730, 785, 801, 842, 865, 901, 962, 969, 973, 1001

Offset: 1

Author

Reinhard Zumkeller, Jul 23 2013

Keywords

• nonn

Comments

A078310 in natural order.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequences: A078325, A078324.

Cf. A001694, A078310, A007947.

Programs

Haskell

a224866 n = a224866_list !! (n-1)
a224866_list = [x | x <- [2..] , let x' = x - 1, let k = a007947 x',
                    let (y,m) = divMod x' k, m == 0, a007947 y == k]

Mathematica

powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Range[1001], powQ[# - 1] &] (* Amiram Eldar, Jul 31 2022 *)

PARI

is(n) = n>1 && ispowerful(n-1) \\ Charles R Greathouse IV, Aug 08 2013, corrected by Amiram Eldar, Jul 31 2022

Formula

a(n) = A001694(n) + 1.