OFFSET
1,1
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)
EXAMPLE
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)
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jamie Morken, May 24 2017
STATUS
approved