cp's OEIS Frontend

A078324 Primes of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).

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