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A324856 Numbers divisible by exactly one of their prime indices.

%I A324856 #10 Mar 23 2019 02:51:25
%S A324856 2,10,14,15,22,26,34,38,45,46,50,55,58,62,70,74,82,86,94,98,105,106,
%T A324856 118,119,122,130,134,135,142,146,154,158,166,170,178,182,190,194,195,
%U A324856 202,206,207,214,218,226,230,242,250,254,255,262,266,274,275,278,285
%N A324856 Numbers divisible by exactly one of their prime indices.
%C A324856 Numbers n such that A324848(n) = 1.
%C A324856 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A324856 If k is in A324846, then k*prime(k) is in the sequence. - _Robert Israel_, Mar 22 2019
%H A324856 Robert Israel, <a href="/A324856/b324856.txt">Table of n, a(n) for n = 1..10000</a>
%e A324856 The sequence of terms together with their prime indices begins:
%e A324856    2: {1}
%e A324856   10: {1,3}
%e A324856   14: {1,4}
%e A324856   15: {2,3}
%e A324856   22: {1,5}
%e A324856   26: {1,6}
%e A324856   34: {1,7}
%e A324856   38: {1,8}
%e A324856   45: {2,2,3}
%e A324856   46: {1,9}
%e A324856   50: {1,3,3}
%e A324856   55: {3,5}
%e A324856   58: {1,10}
%e A324856   62: {1,11}
%e A324856   70: {1,3,4}
%e A324856   74: {1,12}
%e A324856   82: {1,13}
%e A324856   86: {1,14}
%e A324856   94: {1,15}
%e A324856   98: {1,4,4}
%p A324856 filter:= proc(n) local F;
%p A324856   F:= select(t -> n mod numtheory:-pi(t[1])=0, ifactors(n)[2]);
%p A324856   nops(F)=1 and F[1][2]=1
%p A324856 end proc:
%p A324856 select(filter, [$2..1000]); # _Robert Israel_, Mar 22 2019
%t A324856 Select[Range[100],Total[Cases[If[#==1,{},FactorInteger[#]],{p_,k_}:>k/;Divisible[#,PrimePi[p]]]]==1&]
%Y A324856 Cf. A000720, A003963, A112798, A120383, A323440, A324694, A324704, A324846, A324847, A324848, A324849, A324850, A324926, A324929.
%K A324856 nonn
%O A324856 1,1
%A A324856 _Gus Wiseman_, Mar 21 2019