A287390 - OEIS

%I #9 Jul 03 2017 01:52:42

%S 121,143,187,209,221,247,299,377,403,481,533,559,611,689,767,793,871,

%T 923,949,1027,1079,1157,1261,1313,1339,1391,1417,1469,1651,1703,1781,

%U 1807,1937,1963,2041,2119,2171,2197,2249,2329,2363,2533,2567,2669,2771,2839

%N Nonprimes k that are a totative of only one primorial P in A002110.

%C From _Michael De Vlieger_, May 24 2017: (Start)

%C Let p_n# = A002110(n). Composite numbers p_n# < k < p_(n+1)# such that gcd(k,p_(n+1)) = 1 and whose minimum prime divisor is p_(n+2).

%C Subsequence of A285784.

%C The sequence can be thought of as an irregular triangle T(n,k) with the first terms appearing for n = 3. Row lengths of T(n,k) < A048863(n).

%C Many of the terms are semiprimes p_(n+2)*q with p_(n+2) < q < p_pi(p_(n+1)#), where pi(x) = A000720(x).

%C The smallest square in a(n) is 121 = 11^2. The smallest p^m for m = {2, 3, 4, 5} is {121, 2197, 130321, 643343}, which are {11^2, 13^3, 19^4, 23^5} respectively.

%C (End)

%e From _Michael De Vlieger_, May 24 2017: (Start)

%e The numbers 121, 143, 187, and 209 are in the sequence because these are nonprimes greater than p_3# = 30 but less than p_4# = 210 with minimum prime divisor p_5 = 11.

%e The number 169 is not in the sequence because, although it falls between 30 and 210, it is coprime to 210 and to 2310 and thus is a totative of both these primorials.

%e (End)

%t MapIndexed[Select[Range @@ #1, Function[k, Function[f, And[Total[f[[All, -1]]] > 1, CoprimeQ[Last@ #1, k], f[[1, 1]] == Prime[First@ #2 + 1]]]@ FactorInteger[k]]] &, Partition[FoldList[#1 #2 &, 1, Prime@ Range@ 6], 2, 1]] // Flatten (* _Michael De Vlieger_, May 24 2017 *)

%Y Cf. A002110, A048863, A285784.

%K nonn

%O 1,1

%A _Jamie Morken_, May 24 2017