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A324846 Positive integers divisible by none of their prime indices.

%I A324846 #15 Mar 19 2019 19:30:14
%S A324846 1,3,5,7,9,11,13,17,19,21,23,25,27,29,31,33,35,37,39,41,43,47,49,51,
%T A324846 53,57,59,61,63,65,67,69,71,73,77,79,81,83,85,87,89,91,93,95,97,99,
%U A324846 101,103,107,109,111,113,115,117,121,123,125,127,129,131,133,137
%N A324846 Positive integers divisible by none of their prime indices.
%C A324846 A prime index of n is a number m such that prime(m) divides n. For example, the prime indices of 5673 are {2,11,18}, none of which divides 5673, so 5673 belongs to the sequence.
%H A324846 Alois P. Heinz, <a href="/A324846/b324846.txt">Table of n, a(n) for n = 1..10000</a>
%e A324846 The sequence of terms together with their prime indices begins:
%e A324846    1: {}
%e A324846    3: {2}
%e A324846    5: {3}
%e A324846    7: {4}
%e A324846    9: {2,2}
%e A324846   11: {5}
%e A324846   13: {6}
%e A324846   17: {7}
%e A324846   19: {8}
%e A324846   21: {2,4}
%e A324846   23: {9}
%e A324846   25: {3,3}
%e A324846   27: {2,2,2}
%e A324846   29: {10}
%e A324846   31: {11}
%e A324846   33: {2,5}
%e A324846   35: {3,4}
%e A324846   37: {12}
%e A324846   39: {2,6}
%p A324846 q:= n-> ormap(i-> irem(n, numtheory[pi](i[1]))=0, ifactors(n)[2]):
%p A324846 remove(q, [$1..200])[];  # _Alois P. Heinz_, Mar 19 2019
%t A324846 Select[Range[100],!Or@@Cases[If[#==1,{},FactorInteger[#]],{p_,_}:>Divisible[#,PrimePi[p]]]&]
%o A324846 (PARI) isok(n) = {my(f = factor(n)[,1]); for (k=1, #f, if (!(n % primepi(f[k])), return (0));); return (1);} \\ _Michel Marcus_, Mar 19 2019
%Y A324846 Complement of A324847.
%Y A324846 Cf. A000720, A001222, A003963, A056239, A112798, A120383, A289509, A290822, A304360, A306844.
%Y A324846 Cf. A324695, A324741, A324743, A324756, A324758, A324765, A324848, A324849, A324850, A324852, A324853.
%K A324846 nonn
%O A324846 1,2
%A A324846 _Gus Wiseman_, Mar 18 2019