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A328338 Numbers whose third-largest divisor is prime.

%I A328338 #10 Oct 19 2019 20:47:47
%S A328338 6,8,10,14,15,20,21,22,26,27,28,33,34,35,38,39,44,46,51,52,55,57,58,
%T A328338 62,65,68,69,74,76,77,82,85,86,87,91,92,93,94,95,99,106,111,115,116,
%U A328338 117,118,119,122,123,124,125,129,133,134,141,142,143,145,146,148
%N A328338 Numbers whose third-largest divisor is prime.
%H A328338 Antti Karttunen, <a href="/A328338/b328338.txt">Table of n, a(n) for n = 1..10000</a>
%e A328338 The sequence of terms together with their divisors begins:
%e A328338    6: {1,2,3,6}
%e A328338    8: {1,2,4,8}
%e A328338   10: {1,2,5,10}
%e A328338   14: {1,2,7,14}
%e A328338   15: {1,3,5,15}
%e A328338   20: {1,2,4,5,10,20}
%e A328338   21: {1,3,7,21}
%e A328338   22: {1,2,11,22}
%e A328338   26: {1,2,13,26}
%e A328338   27: {1,3,9,27}
%e A328338   28: {1,2,4,7,14,28}
%e A328338   33: {1,3,11,33}
%e A328338   34: {1,2,17,34}
%e A328338   35: {1,5,7,35}
%e A328338   38: {1,2,19,38}
%e A328338   39: {1,3,13,39}
%e A328338   44: {1,2,4,11,22,44}
%e A328338   46: {1,2,23,46}
%e A328338   51: {1,3,17,51}
%e A328338   52: {1,2,4,13,26,52}
%p A328338 q:= n-> (l-> nops(l)>2 and isprime(l[-3]))(
%p A328338          sort([numtheory[divisors](n)[]])):
%p A328338 select(q, [$1..200])[];  # _Alois P. Heinz_, Oct 19 2019
%t A328338 Select[Range[100],Length[Divisors[#]]>2&&PrimeQ[Divisors[#][[-3]]]&]
%o A328338 (PARI) isA328338(n) = { my(u=numdiv(n)); ((u>2)&&isprime(divisors(n)[u-2])); }; \\ _Antti Karttunen_, Oct 17 2019
%Y A328338 A subset of A002808 and superset of A006881.
%Y A328338 Numbers whose third-smallest divisor is prime are A119313.
%Y A328338 Third-smallest divisor is A292269.
%Y A328338 Cf. A000005, A020639, A027750, A033676, A060775, A067513, A088725.
%K A328338 nonn
%O A328338 1,1
%A A328338 _Gus Wiseman_, Oct 16 2019