A287390 Nonprimes k that are a totative of only one primorial P in A002110.

121, 143, 187, 209, 221, 247, 299, 377, 403, 481, 533, 559, 611, 689, 767, 793, 871, 923, 949, 1027, 1079, 1157, 1261, 1313, 1339, 1391, 1417, 1469, 1651, 1703, 1781, 1807, 1937, 1963, 2041, 2119, 2171, 2197, 2249, 2329, 2363, 2533, 2567, 2669, 2771, 2839

Offset: 1

Author

Jamie Morken, May 24 2017

Keywords

• nonn

Comments

From Michael De Vlieger, May 24 2017: (Start)

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).

Subsequence of A285784.

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).

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).

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.

(End)

Examples

			From _Michael De Vlieger_, May 24 2017: (Start)
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.
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.
(End)
		

Crossrefs

Cf. A002110, A048863, A285784.

Programs

Mathematica

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 *)