

A152823


Largest divisor < n of n^2 + 1, a(1) = 1.


1



1, 1, 2, 1, 2, 1, 5, 5, 2, 1, 2, 5, 10, 1, 2, 1, 10, 13, 2, 1, 17, 5, 10, 1, 2, 1, 10, 5, 2, 17, 26, 25, 10, 13, 2, 1, 10, 17, 2, 1, 29, 5, 37, 13, 2, 29, 34, 5, 2, 41, 2, 5, 10, 1, 34, 1, 50, 5, 2, 13, 2, 5, 10, 17, 2, 1, 10, 37, 2, 29, 2, 61, 65, 1, 58, 53, 10, 5, 2, 37, 34, 25, 65, 1, 2, 13
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OFFSET

1,3


COMMENTS

If a(2k) = 3, then 4k^2 + 1 = 3p with p prime. For odd n > 1, a(n) >= 2, with equality if (n^2+1)/2 is prime. Conversely, A147809(n) = 1 iff n^2 + 1 is a semiprime, which for odd n > 1 implies a(n) = 2.
a(1) = 1 by convention, which is compatible with the FORMULA (a(n) = 1 iff n^2 + 1 is prime) and also with a(n) = the floor(d/2)th divisor of n^2+1, when d is its total number of divisors, cf. PROGRAM.  M. F. Hasler, Sep 11 2019


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = 1 iff n^2 + 1 is prime (iff A147809(n)=0), which can only happen for n = 1 or even n.


MATHEMATICA

a[1] = 1; a[n_] := Max[Select[Divisors[n^2 + 1], # < n &]]; Array[a, 100] (* Amiram Eldar, Sep 12 2019 *)


PROG

(PARI) A152823(n)={ n=divisors(n^2+1); n[ #n\2] }


CROSSREFS

Sequence in context: A318360 A102551 A217437 * A324605 A086545 A337395
Adjacent sequences: A152820 A152821 A152822 * A152824 A152825 A152826


KEYWORD

nonn


AUTHOR

M. F. Hasler, Dec 15 2008


STATUS

approved



