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A125271
Number of Gaussian integer divisors of n (having positive real part).
0
1, 4, 2, 7, 6, 8, 2, 10, 3, 20, 2, 14, 6, 8, 12, 13, 6, 12, 2, 34, 4, 8, 2, 20, 15, 20, 4, 14, 6, 40, 2, 16, 4, 20, 12, 21, 6, 8, 12, 48, 6, 16, 2, 14, 18, 8, 2, 26, 3, 48, 12, 34, 6, 16, 12, 20, 4, 20, 2, 68, 6, 8, 6, 19, 28, 16, 2, 34, 4, 40, 2, 30, 6, 20, 30
OFFSET
1,2
COMMENTS
To avoid the redundancy of counting the negatives of the divisors, we consider only divisors having a positive real part.
The usual method of counting complex divisors is to exclude associates. For example, although 1+i and 1-i both divide 2, one is just -i times the other. This sequence counts each first-quadrant complex divisor twice. Sequence A062327 counts those complex divisors only once. - T. D. Noe, Feb 21 2007
LINKS
Eric Weisstein's World of Mathematics, Gaussian Integer.
FORMULA
a(n) = 2*A062327(n) - A000005(n). - T. D. Noe, Feb 21 2007
EXAMPLE
a(5) = 6 because 5 is divisible by the Gaussian integers {1, 1-2i, 1+2i, 2-i, 2+i, 5}, which is 6 divisors in all.
CROSSREFS
Sequence in context: A367832 A307869 A016695 * A245262 A092314 A237750
KEYWORD
easy,nonn
AUTHOR
Mitch Cervinka (puritan(AT)toast.net), Jan 16 2007
STATUS
approved