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%I #29 Apr 27 2017 22:54:49
%S 115,329,1243,2119,2171,4709,4777,4811,6593,6631,6707,6821,11707,
%T 11983,12029,14597,15463,16793,23809,23867,23983,24041,24331,29047,
%U 29171,29357,29543,50357,50579,67937,68183,68347,68429,77873,78389,78733,79421,83351,83453,102413
%N n for which A079277(n) + phi(n) < n.
%C 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
%C From _Antti Karttunen_, Apr 26 2017: (Start)
%C Numbers n for which A051953(n) > A079277(n).
%C 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.
%C (End)
%H David A. Corneth, <a href="/A208815/b208815.txt">Table of n, a(n) for n = 1..1751 (terms up to 87 million)</a>
%e A079277(115) + phi(115) = 25 + 88 = 113 < 115 so 115 is in the sequence, where phi = A000010.
%t 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 *)
%t 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 *)
%Y Positions of negative terms in A285709.
%Y Cf. A000010, A010846, A051953, A079277, A285699, A285710.
%K nonn
%O 1,1
%A _Robert Israel_, Mar 01 2012
%E a(28)-a(29) from _Antti Karttunen_, Apr 26 2017
%E a(30)-a(40) from _David A. Corneth_, Apr 26 2017
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