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A208815
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n for which A079277(n) + phi(n) < n.
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4
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115, 329, 1243, 2119, 2171, 4709, 4777, 4811, 6593, 6631, 6707, 6821, 11707, 11983, 12029, 14597, 15463, 16793, 23809, 23867, 23983, 24041, 24331, 29047, 29171, 29357, 29543, 50357, 50579, 67937, 68183, 68347, 68429, 77873, 78389, 78733, 79421, 83351, 83453, 102413
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OFFSET
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1,1
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COMMENTS
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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
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.
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LINKS
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EXAMPLE
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A079277(115) + phi(115) = 25 + 88 = 113 < 115 so 115 is in the sequence, where phi = A000010.
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MATHEMATICA
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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 *)
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CROSSREFS
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Positions of negative terms in A285709.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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