

A328827


a(n) is the largest prime factor of n + n*(n+1)/2 = n*(n+3)/2.


1



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, 29, 11, 31, 7, 11, 37, 19, 13, 37, 41, 13, 43, 41, 7, 43, 47, 5, 23, 47, 17, 13, 53, 17, 13, 53, 19, 29, 59, 19, 61, 59, 7, 61, 31, 11, 67
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(n) is the largest prime factor of either n or n+3; hence a(p) = p for all prime numbers other than 2.


LINKS

Metin Sariyar, Table of n, a(n) for n = 1..16000


FORMULA

a(n) = A006530(A000096(n)).  Michel Marcus, Oct 28 2019
a(p3) = p for all primes p > 3.  M. F. Hasler, Nov 10 2019


EXAMPLE

For n = 8, n + T(n) = 8 + 36 = 44. The largest prime factor of 44 is 11, so a(8) = 11.


MAPLE

L:=map(max @ numtheory:factorset, [$1..103]):
zip(max, L[1..3], L[4..1]); # Robert Israel, Nov 13 2019


MATHEMATICA

Table[FactorInteger[n+n*(n+1)/2][[1, 1]], {n, 66}] (* Metin Sariyar, Oct 28 2019 *)


PROG

(PARI) a(n)=A006530(n*(n+3)/2) \\ M. F. Hasler, Nov 10 2019
(MAGMA) [Max(PrimeDivisors(n*(n+3) div 2)): n in [1..70]]; // Marius A. Burtea, Nov 13 2019


CROSSREFS

Cf. A000096(n) = n + T(n), A000217(n) = T(n) = n(n+1)/2: triangular numbers, A006530: greatest prime factor.
Sequence in context: A257983 A210770 A227688 * A181184 A078383 A232644
Adjacent sequences: A328824 A328825 A328826 * A328828 A328829 A328830


KEYWORD

nonn


AUTHOR

Ali Sada, Oct 28 2019


EXTENSIONS

Edited by M. F. Hasler, Nov 10 2019


STATUS

approved



