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A161990 Composites which have the same largest prime factor as their index.

%I A161990 #13 Aug 19 2020 09:36:32
%S A161990 10,12,14,25,36,39,42,45,77,124,132,140,147,224,234,266,345,365,370,
%T A161990 375,380,385,390,494,621,638,660,671,682,782,899,945,1001,1086,1140,
%U A161990 1377,1558,1577,1628,1696,1728,1760,1798,1885,2046,2145,2484,2550,2970,3101,3122,3477
%N A161990 Composites which have the same largest prime factor as their index.
%C A161990 If A052369(k) = A006530(k), we add the associated composite A002808(k) to the sequence.
%H A161990 Robert Israel, <a href="/A161990/b161990.txt">Table of n, a(n) for n = 1..4262</a>
%e A161990 The 6th composite is 12=2^2*3 with largest prime factor 3, and the largest prime factor of the index 6=2*3 is also 3, which adds 12 to the sequence.
%e A161990 The 7th composite is 14=2*7 with largest prime factor 7, and the largest prime factor of the index 7 is also 7, which adds 14 to the sequence.
%p A161990 A006530 := proc(n) sort(convert(numtheory[factorset](n),list)); op(-1,%) ; end:
%p A161990 A002808 := proc(n) if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end:
%p A161990 A052369 := proc(n) A006530(A002808(n)) ; end:
%p A161990 for n from 1 to 10000 do if A052369(n) = A006530(n) then printf("%d,",A002808(n)) ; fi; od: # _R. J. Mathar_, Aug 14 2009
%p A161990 # More efficient alternative:
%p A161990 N:= 10000: # to get terms <= N
%p A161990 Lpf:= [seq(max(numtheory:-factorset(n)),n=1..N)]:
%p A161990 comps:= select(n -> Lpf[n]<n, [$4..N]):
%p A161990 map(proc(n) if Lpf[n]=Lpf[comps[n]] then comps[n] fi end proc,
%p A161990 [$1..nops(comps)]); # _Robert Israel_, Mar 05 2018
%t A161990 lpf[n_] := FactorInteger[n ][[-1, 1]];
%t A161990 cc = Select[Range[10000], CompositeQ];
%t A161990 Select[{Range[Length[cc]], cc} // Transpose, lpf[#[[1]]] == lpf[#[[2]]]&][[All, 2]] (* _Jean-François Alcover_, Aug 19 2020 *)
%Y A161990 Cf. A002808, A050696.
%K A161990 nonn
%O A161990 1,1
%A A161990 _Juri-Stepan Gerasimov_, Jun 24 2009
%E A161990 Corrected and extended by _R. J. Mathar_, Aug 14 2009