A070017 Least numbers m such that GCD of two consecutive values of cototients, i.e., gcd(cototient(m+1), cototient(m)) equals 2n - 1.

2, 9, 38, 392, 135, 120, 362, 116, 745, 1183, 294, 528, 1395, 428, 1378, 2602, 1185, 203, 2313, 3042, 1966, 3549, 1431, 551, 7838, 4076, 473, 2635, 903, 2044, 13178, 942, 6819, 12418, 1188, 2264, 3282, 1775, 1517, 2127, 24380, 2884, 2035, 11481

Offset: 1

Author

Labos Elemer and Benoit Cloitre, Apr 12 2002

Keywords

• nonn

Examples

			For n=104: 2n - 1 = 207, a(104) = 235148 because A049586(235148) = 207 and it is the smallest such number. Remark that Count[t=Table[f[w],{w,1,100000}],1]=83132. This suggests that majority of values in A049586 equals one.
		

Crossrefs

Cf. A051953.

Programs

Mathematica

With[{s = Array[# - EulerPhi@ # &, 10^5]}, Function[t, MapAt[# + 1 &, TakeWhile[#, # > 0 &], 1] &@ Table[First[FirstPosition[t, n] /. k_ /; MissingQ@ k -> {0}], {n, 1, Max@ t, 2}]]@ Map[GCD @@ # &@ # &, Partition[s, 2, 1]]] (* Michael De Vlieger, Jul 30 2017 *)

Formula

a(n) = min{x; A049586(x) = 2n - 1}.