A208815 n for which A079277(n) + phi(n) < n.

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

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)

Numbers n for which A051953(n) > A079277(n).

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

A079277(115) + phi(115) = 25 + 88 = 113 < 115 so 115 is in the sequence, where phi = A000010.

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

Positions of negative terms in A285709.

Cf. A000010, A010846, A051953, A079277, A285699, A285710.

Sequence in context: A122562 A063361 A340098 * A334345 A255143 A154070

Adjacent sequences: A208812 A208813 A208814 * A208816 A208817 A208818

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