A259172 - OEIS

%I #27 Jul 17 2015 15:09:53

%S 561,595,1105,1235,1245,1495,1547,1885,2405,2555,2717,2849,3115,3495,

%T 3655,3657,3689,3815,4521,4795,4945,5035,5385,5395,5453,5457,5709,

%U 5865,6083,6141,6251,6285,6365,6391,6501,6695,6755,6969,7021,7887,8113,8255,8355

%N Numbers in A259145 that are neither prime nor semiprime.

%C Regarding the distribution: Let K be the union of primes and semiprimes in A259145. Let S be the set of other terms. The growth rate of the cardinality of S with respect to the cardinality of K is significantly slower. For instance, if we take the first 50000 terms of A259145, about 32.5 percent are contained in S. If we take the first 350000 terms, about 38.2 percent are contained in S.

%C a(n) that are in A002997 (Carmichael numbers) for a(n) <= 10^6 are 561, 1105, 8911, 10585, 29341, 825265.

%C a(n) that are in A051015 (Zeisel numbers) for a(n) <= 3*10^6 are 1885, 353977, 2953711.

%H Carlos Eduardo Olivieri, <a href="/A259172/b259172.txt">Table of n, a(n) for n = 1..8906</a>

%H Eric Naslund, <a href="http://arxiv.org/abs/1203.2363">Integers with a predetermined prime factorization</a>, arXiv:1203.2363 [math.NT], 2012.

%F A001221(a(n)) > 2.

%F A000005(a(n)) = 2^k, k >= 3.

%t Select[Range[25000], PrimeQ[#^2 - EulerPhi[#]] && PrimeNu[#] > 2 &]

%Y Cf. A001221, A001358, A002997, A007053, A051015, A125527, A259145.

%Y Subsequence of A000469, A033942, A050384 (conjuctered).

%K nonn,easy

%O 1,1

%A _Carlos Eduardo Olivieri_, Jun 19 2015