A324847 - OEIS

%I #10 Mar 19 2019 17:38:47

%S 2,4,6,8,10,12,14,15,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,45,

%T 46,48,50,52,54,55,56,58,60,62,64,66,68,70,72,74,75,76,78,80,82,84,86,

%U 88,90,92,94,96,98,100,102,104,105,106,108,110,112,114,116

%N Numbers divisible by at least one of their prime indices.

%C A prime index of n is a number m such that prime(m) divides n.

%C If n is in the sequence, then so are all multiples of n. - _Robert Israel_, Mar 19 2019

%H Robert Israel, <a href="/A324847/b324847.txt">Table of n, a(n) for n = 1..10000</a>

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

%e    2: {1}

%e    4: {1,1}

%e    6: {1,2}

%e    8: {1,1,1}

%e   10: {1,3}

%e   12: {1,1,2}

%e   14: {1,4}

%e   15: {2,3}

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

%e   18: {1,2,2}

%e   20: {1,1,3}

%e   22: {1,5}

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

%e   26: {1,6}

%e   28: {1,1,4}

%e   30: {1,2,3}

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

%e   34: {1,7}

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

%p filter:= proc(n) local F;

%p   F:= map(numtheory:-pi, numtheory:-factorset(n));

%p   ormap(t -> n mod t = 0, F);

%p end proc:

%p select(filter, [$1..200]); # _Robert Israel_, Mar 19 2019

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

%o (PARI) isok(n) = {my(f = factor(n)[,1]); for (k=1, #f, if (!(n % primepi(f[k])), return (1));); return (0);} \\ _Michel Marcus_, Mar 19 2019

%Y Complement of A324846.

%Y Cf. A003963, A056239, A112798, A120383, A289509, A290822, A304360, A306844.

%Y Cf. A324695, A324741, A324743, A324847, A324756, A324758, A324765, A324848, A324849, A324850, A324852, A324853.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 18 2019