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

2, 5, 17, 37, 73, 101, 109, 197, 257, 401, 433, 577, 677, 1153, 1297, 1373, 1601, 1801, 2593, 2917, 3137, 3457, 3529, 3889, 4001, 4357, 5477, 7057, 8101, 8713, 8837, 9001, 10369, 12101, 13457, 14401, 15377, 15877, 16001, 16901, 17497, 17957, 18253, 18433, 20809

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Examples

			12*rad(12)+1 = 12*rad(3*2^2)+1 = 12*3*2+1 = 72+1 = 73, therefore 73 is a term.
a(33) = 10369 = 10368 + 1: A078310(1728) = (2*3)*(2^6*3^3) = 10368.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A000040 and A224866.

Cf. A010051, A078310, A078325.

Programs

Haskell

a078324 n = a078324_list !! (n-1)
a078324_list = filter ((== 1) . a010051') a224866_list
-- Reinhard Zumkeller, Jul 23 2013

Mathematica

powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Prime[Range[2400]], powQ[# - 1] &] (* Amiram Eldar, Jul 31 2022 *)

PARI

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

Extensions

Missing terms 10369, 16001, 17497 and 18433 inserted by Reinhard Zumkeller, Jul 23 2013