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A323440 Numbers divisible by exactly one of their distinct prime indices.

%I A323440 #13 Apr 14 2021 03:13:06
%S A323440 2,4,8,10,14,15,16,20,22,26,32,34,38,40,44,45,46,50,52,55,58,62,64,68,
%T A323440 70,74,75,76,80,82,86,88,92,94,98,100,104,105,106,116,118,119,122,124,
%U A323440 128,130,134,135,136,142,146,148,154,158,160,164,166,170,172,176
%N A323440 Numbers divisible by exactly one of their distinct prime indices.
%C A323440 Numbers n such that A324852(n) = 1.
%C A323440 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.
%H A323440 Amiram Eldar, <a href="/A323440/b323440.txt">Table of n, a(n) for n = 1..10000</a>
%e A323440 The sequence of terms together with their prime indices begins:
%e A323440    2: {1}
%e A323440    4: {1,1}
%e A323440    8: {1,1,1}
%e A323440   10: {1,3}
%e A323440   14: {1,4}
%e A323440   15: {2,3}
%e A323440   16: {1,1,1,1}
%e A323440   20: {1,1,3}
%e A323440   22: {1,5}
%e A323440   26: {1,6}
%e A323440   32: {1,1,1,1,1}
%e A323440   34: {1,7}
%e A323440   38: {1,8}
%e A323440   40: {1,1,1,3}
%e A323440   44: {1,1,5}
%e A323440   45: {2,2,3}
%e A323440   46: {1,9}
%e A323440   50: {1,3,3}
%e A323440   52: {1,1,6}
%e A323440   55: {3,5}
%t A323440 Select[Range[100],Count[If[#==1,{},FactorInteger[#]],{p_,_}/;Divisible[#,PrimePi[p]]]==1&]
%o A323440 (PARI) isok(n) = my(f=factor(n)[,1]); sum(k=1, #f, (n % primepi(f[k])) == 0) == 1; \\ _Michel Marcus_, Mar 22 2019
%Y A323440 Cf. A000720, A003963, A112798, A120383, A324704, A324846, A324847, A324848, A324849, A324850, A324856, A324926, A324929.
%K A323440 nonn
%O A323440 1,1
%A A323440 _Gus Wiseman_, Mar 21 2019