A332839 - OEIS

%I #8 Feb 26 2020 04:00:49

%S 1,2,3,4,6,8,12,18,24,30,5,10,14,20,42,60,7,9,16,36,48,90,15,22,54,84,

%T 26,28,66,120,11,21,32,40,72,78,210,13,34,50,38,44,70,150,102,114,126,

%U 17,27,46,56,96,108,180,19,33,52,132,25,45,80,168,0,23,39,58,62,110,138

%N Irregular triangle whose n-th row lists the integers x such that the number of nonprimes (i.e., 1 and composites) in the reduced residue set (RSS(x)) of x equals n, or 0 if there are no such x.

%H Abhijit A J, A. Satyanarayana Reddy, <a href="https://arxiv.org/abs/1907.09908">Number of non-primes in the set of units modulo n</a>, arXiv:1907.09908 [math.GM], 2019. See p. 3.

%e Triangle begins:

%e 1, 2, 3, 4, 6, 8, 12, 18, 24, 30;

%e 5, 10, 14, 20, 42, 60;

%e 7, 9, 16, 36, 48, 90;

%e 15, 22, 54, 84;

%e 26, 28, 66, 120;

%e 11, 21, 32, 40, 72, 78, 210;

%e ...

%t t = Select[ Table[{ EulerPhi[n] - PrimePi[n] + PrimeNu[n], n}, {n, 2000}], #[[1]] <= 100 &]; c = Complement[Range[100], First /@ t]; Last /@ (Sort@ Join[ Transpose[{c, 0 c}], t]) (* _Giovanni Resta_, Feb 26 2020 *)

%Y Cf. A048597 (1st row), A072022 (least x), A074915 (largest x), A076366 (row lengths).

%K nonn,tabf

%O 1,2

%A _Michel Marcus_, Feb 26 2020