A289172 - OEIS

A289172

Irregular triangle read by rows: row n lists terms m of A038566(n) such that A001221(m) = A051265(n), with a(1) = 1.

%I #11 Aug 26 2017 08:23:42

%S 1,1,2,3,2,3,4,5,6,3,5,7,2,4,5,7,8,3,7,9,6,10,5,7,11,6,10,12,3,5,9,11,

%T 13,14,15,6,10,12,14,15,5,7,11,13,17,6,10,12,14,15,18,3,7,9,11,13,17,

%U 19,10,20,15,21,6,10,12,14,15,18,20,21,22,5,7,11

%N Irregular triangle read by rows: row n lists terms m of A038566(n) such that A001221(m) = A051265(n), with a(1) = 1.

%C Consider A051265(n), the largest value of A001221(m) for 1 <= m <= n such that gcd(m, n) = 1 (i.e., m is in the reduced residue system or RRS of n, or m is a totative of n). Row n of this sequence consists of m in RRS(n) such that omega(m) = A051265(n).

%H Michael De Vlieger, <a href="/A289172/b289172.txt">Table of n, a(n) for the first 1000 rows, flattened</a>

%e Triangle begins:

%e n T(n,m) A051265(n)

%e 1: 1 0

%e 2: 1 0

%e 3: 2 1

%e 4: 3 1

%e 5: 2 3 4 1

%e 6: 5 1

%e 7: 6 2

%e 8: 3 5 7 1

%e 9: 2 4 5 7 8 1

%e 10: 3 7 9 1

%e 11: 6 10 2

%e 12: 5 7 11 1

%e 13: 6 10 12 2

%e 14: 3 5 9 11 13 1

%e 15: 14 2

%e 16: 15 2

%e 17: 6 10 12 14 15 2

%e 18: 5 7 11 13 17 1

%e 19: 6 10 12 14 15 18 2

%e 20: 3 7 9 11 13 17 19 1

%t Table[MaximalBy[#, Last][[All, 1]] &@ Map[{#, PrimeNu@ #} &, Cases[Range[n - 1], k_ /; CoprimeQ[n, k]]] /. {} -> {1}, {n, 30}] // Flatten (* _Michael De Vlieger_, Aug 11 2017 *)

%Y Cf. A001221, A002110, A038566, A048597, A051250, A051265, A051266, A051267, A051268.

%K nonn,easy,tabf

%O 1,3

%A _Michael De Vlieger_, Aug 11 2017