login
Squarefree numbers of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).
7

%I #14 Jul 31 2022 07:46:05

%S 2,5,10,17,26,33,37,65,73,82,101,109,122,129,145,170,197,201,217,226,

%T 257,290,362,393,401,433,442,485,501,530,577,626,649,677,730,785,842,

%U 865,901,962,969,973,1001,1090,1126,1153,1157,1226,1297,1353,1370,1373

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

%H Reinhard Zumkeller, <a href="/A078325/b078325.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Haskell)

%o a078325 n = a078325_list !! (n-1)

%o a078325_list = filter ((== 1) . a008966) a224866_list

%o -- _Reinhard Zumkeller_, Jul 23 2013

%o (PARI) is(n) = n>1 && issquarefree(n) && ispowerful(n-1); \\ _Amiram Eldar_, Jul 31 2022

%Y Intersection of A005117 and A224866.

%Y Cf. A008966, A078310, A078324.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 23 2002