cp's OEIS Frontend

A324847 Numbers divisible by at least one of their prime indices.

%I A324847 #10 Mar 19 2019 17:38:47
%S A324847 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 A324847 46,48,50,52,54,55,56,58,60,62,64,66,68,70,72,74,75,76,78,80,82,84,86,
%U A324847 88,90,92,94,96,98,100,102,104,105,106,108,110,112,114,116
%N A324847 Numbers divisible by at least one of their prime indices.
%C A324847 A prime index of n is a number m such that prime(m) divides n.
%C A324847 If n is in the sequence, then so are all multiples of n. - _Robert Israel_, Mar 19 2019
%H A324847 Robert Israel, <a href="/A324847/b324847.txt">Table of n, a(n) for n = 1..10000</a>
%e A324847 The sequence of terms together with their prime indices begins:
%e A324847    2: {1}
%e A324847    4: {1,1}
%e A324847    6: {1,2}
%e A324847    8: {1,1,1}
%e A324847   10: {1,3}
%e A324847   12: {1,1,2}
%e A324847   14: {1,4}
%e A324847   15: {2,3}
%e A324847   16: {1,1,1,1}
%e A324847   18: {1,2,2}
%e A324847   20: {1,1,3}
%e A324847   22: {1,5}
%e A324847   24: {1,1,1,2}
%e A324847   26: {1,6}
%e A324847   28: {1,1,4}
%e A324847   30: {1,2,3}
%e A324847   32: {1,1,1,1,1}
%e A324847   34: {1,7}
%e A324847   36: {1,1,2,2}
%p A324847 filter:= proc(n) local F;
%p A324847   F:= map(numtheory:-pi, numtheory:-factorset(n));
%p A324847   ormap(t -> n mod t = 0, F);
%p A324847 end proc:
%p A324847 select(filter, [$1..200]); # _Robert Israel_, Mar 19 2019
%t A324847 Select[Range[100],Or@@Cases[If[#==1,{},FactorInteger[#]],{p_,_}:>Divisible[#,PrimePi[p]]]&]
%o A324847 (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 A324847 Complement of A324846.
%Y A324847 Cf. A003963, A056239, A112798, A120383, A289509, A290822, A304360, A306844.
%Y A324847 Cf. A324695, A324741, A324743, A324847, A324756, A324758, A324765, A324848, A324849, A324850, A324852, A324853.
%K A324847 nonn
%O A324847 1,1
%A A324847 _Gus Wiseman_, Mar 18 2019