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%I #39 Sep 08 2022 08:46:24
%S 2,5,3,7,5,3,7,11,3,13,11,5,13,17,5,19,17,7,19,23,7,11,23,3,7,29,5,31,
%T 29,11,31,7,11,37,19,13,37,41,13,43,41,7,43,47,5,23,47,17,13,53,17,13,
%U 53,19,29,59,19,61,59,7,61,31,11,67
%N a(n) is the largest prime factor of n + n*(n+1)/2 = n*(n+3)/2.
%C a(n) is the largest prime factor of either n or n+3; hence a(p) = p for all prime numbers other than 2.
%H Metin Sariyar, <a href="/A328827/b328827.txt">Table of n, a(n) for n = 1..16000</a>
%F a(n) = A006530(A000096(n)). - _Michel Marcus_, Oct 28 2019
%F a(p-3) = p for all primes p > 3. - _M. F. Hasler_, Nov 10 2019
%e For n = 8, n + T(n) = 8 + 36 = 44. The largest prime factor of 44 is 11, so a(8) = 11.
%p L:=map(max @ numtheory:-factorset, [$1..103]):
%p zip(max, L[1..-3],L[4..-1]);# _Robert Israel_, Nov 13 2019
%t Table[FactorInteger[n+n*(n+1)/2][[-1, 1]], {n,66}] (* _Metin Sariyar_, Oct 28 2019 *)
%o (PARI) a(n)=A006530(n*(n+3)/2) \\ _M. F. Hasler_, Nov 10 2019
%o (Magma) [Max(PrimeDivisors(n*(n+3) div 2)): n in [1..70]]; // _Marius A. Burtea_, Nov 13 2019
%Y Cf. A000096(n) = n + T(n), A000217(n) = T(n) = n(n+1)/2: triangular numbers, A006530: greatest prime factor.
%K nonn
%O 1,1
%A _Ali Sada_, Oct 28 2019
%E Edited by _M. F. Hasler_, Nov 10 2019
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