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

1,1

Links

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

Example

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.

Mathematica

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

Prog

(Haskell)
a078324 n = a078324_list !! (n-1)
a078324_list = filter ((== 1) . a010051') a224866_list
-- Reinhard Zumkeller, Jul 23 2013
(PARI) is(n) = isprime(n) && ispowerful(n-1); \\ Amiram Eldar, Jul 31 2022

Crossrefs

Intersection of A000040 and A224866.

Cf. A010051, A078310, A078325.

Sequence in context: A100272 A107630 A078523 * A240322 A346809 A276460

Adjacent sequences: A078321 A078322 A078323 * A078325 A078326 A078327

Keyword

nonn

Author

Reinhard Zumkeller, Nov 23 2002

Extensions

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

Status

approved