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%I #14 Jul 31 2022 07:45:59
%S 2,5,17,37,73,101,109,197,257,401,433,577,677,1153,1297,1373,1601,
%T 1801,2593,2917,3137,3457,3529,3889,4001,4357,5477,7057,8101,8713,
%U 8837,9001,10369,12101,13457,14401,15377,15877,16001,16901,17497,17957,18253,18433,20809
%N Primes of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).
%H Reinhard Zumkeller, <a href="/A078324/b078324.txt">Table of n, a(n) for n = 1..1000</a>
%e 12*rad(12)+1 = 12*rad(3*2^2)+1 = 12*3*2+1 = 72+1 = 73, therefore 73 is a term.
%e a(33) = 10369 = 10368 + 1: A078310(1728) = (2*3)*(2^6*3^3) = 10368.
%t powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Prime[Range[2400]], powQ[# - 1] &] (* _Amiram Eldar_, Jul 31 2022 *)
%o (Haskell)
%o a078324 n = a078324_list !! (n-1)
%o a078324_list = filter ((== 1) . a010051') a224866_list
%o -- _Reinhard Zumkeller_, Jul 23 2013
%o (PARI) is(n) = isprime(n) && ispowerful(n-1); \\ _Amiram Eldar_, Jul 31 2022
%Y Intersection of A000040 and A224866.
%Y Cf. A010051, A078310, A078325.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Nov 23 2002
%E Missing terms 10369, 16001, 17497 and 18433 inserted by _Reinhard Zumkeller_, Jul 23 2013