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A324850 Numbers divisible by the product of their prime indices.

%I A324850 #17 Apr 14 2021 04:20:21
%S A324850 1,2,4,6,8,12,16,24,28,30,32,36,48,56,60,64,72,96,112,120,128,144,152,
%T A324850 156,168,180,192,216,224,240,256,288,304,312,330,336,360,384,432,448,
%U A324850 476,480,512,576,608,624,660,672,720,768,784,828,840,848,864,888,896
%N A324850 Numbers divisible by the product of their prime indices.
%C A324850 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, with product A003963(n). For example, the prime indices of 30 are {1,2,3}, with product 6, which divides 30, so 30 is in the sequence.
%H A324850 Amiram Eldar, <a href="/A324850/b324850.txt">Table of n, a(n) for n = 1..10000</a>
%F A324850 n/A003963(n) = A324933(n)/A324934(n).
%e A324850 The sequence of terms together with their prime indices begins:
%e A324850    1: {}
%e A324850    2: {1}
%e A324850    4: {1,1}
%e A324850    6: {1,2}
%e A324850    8: {1,1,1}
%e A324850   12: {1,1,2}
%e A324850   16: {1,1,1,1}
%e A324850   24: {1,1,1,2}
%e A324850   28: {1,1,4}
%e A324850   30: {1,2,3}
%e A324850   32: {1,1,1,1,1}
%e A324850   36: {1,1,2,2}
%e A324850   48: {1,1,1,1,2}
%e A324850   56: {1,1,1,4}
%e A324850   60: {1,1,2,3}
%e A324850   64: {1,1,1,1,1,1}
%e A324850   72: {1,1,1,2,2}
%e A324850   96: {1,1,1,1,1,2}
%t A324850 Select[Range[100],Divisible[#,Times@@Cases[If[#==1,{},FactorInteger[#]],{p_,k_}:>PrimePi[p]^k]]&]
%o A324850 (PARI) isok(n) = my(f=factor(n)); !(n % prod(k=1, #f~, primepi(f[k,1])^f[k,2])); \\ _Michel Marcus_, Mar 22 2019
%Y A324850 Cf. A003963, A036844, A120383, A324847, A324756, A324758, A324847, A324848, A324849, A324852, A324853, A324856, A324923, A324924, A324925, A324931.
%K A324850 nonn
%O A324850 1,2
%A A324850 _Gus Wiseman_, Mar 18 2019