A152823 - OEIS

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A152823

Largest divisor < n of n^2+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 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`a(n)=1 iff n^2+1 is prime (iff A147809(n)=0), which can only happen for n=1 or even n. 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.`
	PROG	`(PARI) A152823(n)={ n=divisors(n^2+1); n[ #n\2] }`
	CROSSREFS	`Sequence in context: A109087 A102048 A102551 * A086545 A126083 A071416` `Adjacent sequences: A152820 A152821 A152822 * A152824 A152825 A152826`
	KEYWORD	`nonn`
	AUTHOR	`M. F. Hasler (www.univ-ag.fr/~mhasler), Dec 15 2008`

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Last modified February 14 03:37 EST 2012. Contains 205570 sequences.