OFFSET
1,1
COMMENTS
Includes (among other terms, see below) semiprimes pq where p and q are primes with p^k-p+1 < q < p^k for an integer k>1. In particular, by the Prime Number Theorem this sequence is infinite. - clarified by Antti Karttunen, Apr 26 2017
From Antti Karttunen, Apr 26 2017: (Start)
Factorization of terms a(1) .. a(29): 5*23, 7*47, 11*113, 13*163, 13*167, 17*277, 17*281, 17*283, 19*347, 19*349, 19*353, 19*359, 23*509, 23*521, 23*523, 11*1327, 7*47*47, 7*2399, 29*821, 29*823, 29*827, 29*829, 29*839, 31*937, 31*941, 31*947, 31*953, 37*1361, 37*1367. Note that a(17) = 15463 is not a semiprime.
(End)
LINKS
David A. Corneth, Table of n, a(n) for n = 1..1751 (terms up to 87 million)
EXAMPLE
MATHEMATICA
Select[Range[2, 10^4], Function[n, If[n == 2, 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]] + EulerPhi@ n < n]] (* or *)
Do[If[If[n == 2, 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]] + EulerPhi@ n < n, Print@ n], {n, 2, 10^5}] (* Michael De Vlieger, Apr 27 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Mar 01 2012
EXTENSIONS
a(28)-a(29) from Antti Karttunen, Apr 26 2017
a(30)-a(40) from David A. Corneth, Apr 26 2017
STATUS
approved