A252489 Index of the largest prime which divides n*(n+1).

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

Offset: 1

Author

M. F. Hasler, Jan 16 2015

Keywords

• nonn
• look

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

A061395:= [1, seq(numtheory:-pi(max(numtheory:-factorset(n))), n=2..101)]:
zip(max,A061395[1..-2],A061395[2..-1]); # Robert Israel, Feb 12 2021

Mathematica

a[n_] := PrimePi[Max[FactorInteger[n][[-1, 1]], FactorInteger[n+1][[-1, 1]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 05 2023 *)

PARI

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

Formula

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

a(n) = max(A061395(n),A061395(n+1)). - Robert Israel, Feb 12 2021