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A147809 Half the number of proper divisors (> 1) of n^2 + 1, i.e., tau(n^2 + 1)/2 - 1. 6
0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 3, 0, 1, 0, 3, 2, 1, 0, 3, 1, 3, 0, 1, 0, 3, 1, 1, 1, 3, 2, 3, 1, 1, 0, 3, 2, 1, 0, 2, 1, 5, 1, 1, 1, 7, 1, 1, 1, 1, 1, 3, 0, 3, 0, 7, 1, 1, 1, 1, 1, 3, 1, 1, 0, 3, 3, 1, 2, 1, 3, 7, 0, 3, 1, 3, 1, 1, 1, 3, 2, 7, 0, 1, 1, 3, 1, 3, 0, 3, 1, 5, 0, 1, 1, 3, 3, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

For any n > 0, n^2 + 1 cannot be a square and thus has an even number of divisors which always include 1 and n^2 + 1, therefore a(n) = (half that number minus 1) is always a nonnegative integer.

LINKS

Table of n, a(n) for n=1..99.

FORMULA

a(n) = A000005(A002522(n))/2 - 1 = A147810(n) - 1.

MATHEMATICA

DivisorSigma[0, Range[100]^2+1]/2-1 (* Harvey P. Dale, Feb 11 2015 *)

PROG

(PARI) A147809(n)=numdiv(n^2+1)/2-1

CROSSREFS

Cf. A048691, A063647.

Sequence in context: A156749 A325280 A039803 * A325144 A217605 A096651

Adjacent sequences:  A147806 A147807 A147808 * A147810 A147811 A147812

KEYWORD

easy,nonn

AUTHOR

M. F. Hasler, Dec 13 2008

STATUS

approved

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Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)