A078325 Squarefree numbers of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).

2, 5, 10, 17, 26, 33, 37, 65, 73, 82, 101, 109, 122, 129, 145, 170, 197, 201, 217, 226, 257, 290, 362, 393, 401, 433, 442, 485, 501, 530, 577, 626, 649, 677, 730, 785, 842, 865, 901, 962, 969, 973, 1001, 1090, 1126, 1153, 1157, 1226, 1297, 1353, 1370, 1373

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Links

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

Crossrefs

Intersection of A005117 and A224866.

Cf. A008966, A078310, A078324.

Programs

Haskell

a078325 n = a078325_list !! (n-1)
a078325_list = filter ((== 1) . a008966) a224866_list
-- Reinhard Zumkeller, Jul 23 2013

Mathematica

powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Range[1400], SquareFreeQ[#] && powQ[# - 1] &] (* Amiram Eldar, Jul 31 2022 *)

PARI

is(n) = n>1 && issquarefree(n) && ispowerful(n-1); \\ Amiram Eldar, Jul 31 2022