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A324856 Numbers divisible by exactly one of their prime indices. 9

%I #10 Mar 23 2019 02:51:25

%S 2,10,14,15,22,26,34,38,45,46,50,55,58,62,70,74,82,86,94,98,105,106,

%T 118,119,122,130,134,135,142,146,154,158,166,170,178,182,190,194,195,

%U 202,206,207,214,218,226,230,242,250,254,255,262,266,274,275,278,285

%N Numbers divisible by exactly one of their prime indices.

%C Numbers n such that A324848(n) = 1.

%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.

%C If k is in A324846, then k*prime(k) is in the sequence. - _Robert Israel_, Mar 22 2019

%H Robert Israel, <a href="/A324856/b324856.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 10: {1,3}

%e 14: {1,4}

%e 15: {2,3}

%e 22: {1,5}

%e 26: {1,6}

%e 34: {1,7}

%e 38: {1,8}

%e 45: {2,2,3}

%e 46: {1,9}

%e 50: {1,3,3}

%e 55: {3,5}

%e 58: {1,10}

%e 62: {1,11}

%e 70: {1,3,4}

%e 74: {1,12}

%e 82: {1,13}

%e 86: {1,14}

%e 94: {1,15}

%e 98: {1,4,4}

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

%p F:= select(t -> n mod numtheory:-pi(t[1])=0, ifactors(n)[2]);

%p nops(F)=1 and F[1][2]=1

%p end proc:

%p select(filter, [$2..1000]); # _Robert Israel_, Mar 22 2019

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

%Y Cf. A000720, A003963, A112798, A120383, A323440, A324694, A324704, A324846, A324847, A324848, A324849, A324850, A324926, A324929.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 21 2019

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Last modified March 28 14:02 EDT 2024. Contains 371254 sequences. (Running on oeis4.)