%I #17 Apr 14 2021 04:20:21

%S 1,2,4,6,8,12,16,24,28,30,32,36,48,56,60,64,72,96,112,120,128,144,152,

%T 156,168,180,192,216,224,240,256,288,304,312,330,336,360,384,432,448,

%U 476,480,512,576,608,624,660,672,720,768,784,828,840,848,864,888,896

%N Numbers divisible by the product of their prime indices.

%C 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 Amiram Eldar, <a href="/A324850/b324850.txt">Table of n, a(n) for n = 1..10000</a>

%F n/A003963(n) = A324933(n)/A324934(n).

%e The sequence of terms together with their prime indices begins:

%e 1: {}

%e 2: {1}

%e 4: {1,1}

%e 6: {1,2}

%e 8: {1,1,1}

%e 12: {1,1,2}

%e 16: {1,1,1,1}

%e 24: {1,1,1,2}

%e 28: {1,1,4}

%e 30: {1,2,3}

%e 32: {1,1,1,1,1}

%e 36: {1,1,2,2}

%e 48: {1,1,1,1,2}

%e 56: {1,1,1,4}

%e 60: {1,1,2,3}

%e 64: {1,1,1,1,1,1}

%e 72: {1,1,1,2,2}

%e 96: {1,1,1,1,1,2}

%t Select[Range[100],Divisible[#,Times@@Cases[If[#==1,{},FactorInteger[#]],{p_,k_}:>PrimePi[p]^k]]&]

%o (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 Cf. A003963, A036844, A120383, A324847, A324756, A324758, A324847, A324848, A324849, A324852, A324853, A324856, A324923, A324924, A324925, A324931.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 18 2019