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%I #10 Sep 08 2022 08:45:46
%S 4,7,8,9,11,13,15,17,16,19,21,22,23,25,25,27,27,29,31,32,35,35,37,37,
%T 39,40,41,43,45,47,47,49,49,51,53,53,55,56,57,58,59,61,63,64,64,68,67,
%U 69,71,71,73,75,77,77,81,79,81,81,83,85,87,87,89,89,91,97,93,94,95,99,97
%N a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).
%C Auxiliary sequence for A161850, which is the subsequence consisting of all terms that are prime.
%C a(n) = A002808(n)+A161849(n).
%H Bill McEachen, <a href="/A161986/b161986.txt">Table of n, a(n) for n = 1..10000</a>
%e n = 1: composite(1) = 4; (largest prime divisor of 4) = (smallest prime divisor 4) = 2; 2 mod 2 = 0. Hence a(1) = 4+0 = 4.
%e n = 5: composite(5) = 10; (largest prime divisor of 10) = 5; (smallest prime divisor 10) = 2; 5 mod 2 = 1. Hence a(5) = 10+1 = 11.
%o (Magma) [ n + D[ #D] mod D[1]: n in [2..100] | not IsPrime(n) where D is PrimeDivisors(n) ];
%o (PARI) genit(maxx=1000)={ctr=0;arr=List();forcomposite(k=4,+oo,v=factor(k)[,1];r=v[#v]%v[1];ctr+=1;if(ctr>=maxx,break);listput(arr,k+r));arr} \\ _Bill McEachen_, Nov 17 2021
%Y Cf. A161850, A002808 (composite numbers), A052369 (largest prime factor of n-th composite), A056608 (smallest divisor of n-th composite), A161849 (A052369(n) mod A056608(n)).
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Jun 23 2009
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