A252489 - OEIS

%I #17 Dec 05 2023 19:47:05

%S 1,2,2,3,3,4,4,2,3,5,5,6,6,4,3,7,7,8,8,4,5,9,9,3,6,6,4,10,10,11,11,5,

%T 7,7,4,12,12,8,6,13,13,14,14,5,9,15,15,4,4,7,7,16,16,5,5,8,10,17,17,

%U 18,18,11,4,6,6,19,19,9,9,20,20,21,21,12,8,8,6

%N Index of the largest prime which divides n*(n+1).

%C Yields the row of A145605 in which n appears, and also the first row of A138180 in which n appears.

%H Robert Israel, <a href="/A252489/b252489.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = pi(A074399(n)), where pi = A000720.

%F a(n) = max(A061395(n),A061395(n+1)). - _Robert Israel_, Feb 12 2021

%p A061395:= [1, seq(numtheory:-pi(max(numtheory:-factorset(n))), n=2..101)]:

%p zip(max,A061395[1..-2],A061395[2..-1]); # _Robert Israel_, Feb 12 2021

%t a[n_] := PrimePi[Max[FactorInteger[n][[-1, 1]], FactorInteger[n+1][[-1, 1]]]];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Dec 05 2023 *)

%o (PARI) a(n)=primepi(vecmax(factor(n*(n+1))[,1]))

%Y Cf. A002071, A145604, A138180, A145605, A002072, A074399, A061395.

%K nonn,look

%O 1,2

%A _M. F. Hasler_, Jan 16 2015