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A078324
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Primes of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).
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5
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
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EXAMPLE
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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.
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MATHEMATICA
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powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Prime[Range[2400]], powQ[# - 1] &] (* Amiram Eldar, Jul 31 2022 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Nov 23 2002
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EXTENSIONS
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Missing terms 10369, 16001, 17497 and 18433 inserted by Reinhard Zumkeller, Jul 23 2013
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STATUS
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approved
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