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A152990
Sum of proper divisors minus the number of proper divisors of Fibonacci number A000045(n).
4
0, 0, 0, 0, 0, 4, 0, 8, 17, 14, 0, 245, 0, 40, 499, 542, 0, 2801, 148, 5316, 6771, 286, 0, 110809, 18032, 752, 124327, 155934, 0, 1310617, 2972, 1213164, 1821955, 5166, 2697336, 33280689, 506376, 1416024, 32030851, 106878198, 62156, 295708841, 0
OFFSET
1,6
COMMENTS
Note that if a(n) != 0 then Fibonacci number A000045(n) is a composite number (A002808), otherwise A000045(n) is a noncomposite number (A008578). See A152770.
LINKS
Georg Fischer, Table of n, a(n) for n = 1..80 [first 78 terms from B. D. Swan]
FORMULA
a(n) = A000203(A000045(n)) - A000005(A000045(n)) - n + 1 = A001065(A000045(n)) - A032741(A000045(n)) = A152770(A000045(n)).
EXAMPLE
a(8)=8 because Fibonacci(8)=21, the proper divisors of 21 are 1,3 and 7; consequently, a(8) = 1 + 3 + 7 - 3 = 8. - Emeric Deutsch, Jan 02 2009
MAPLE
with(combinat): with(numtheory): seq(sigma(fibonacci(n))-fibonacci(n)-tau(fibonacci(n))+1, n = 1 .. 45); # Emeric Deutsch, Jan 02 2009
PROG
(Magma) [DivisorSigma(1, f)-f-DivisorSigma(0, f)+1 where f is Fibonacci(n):n in [1..43] ]; // Marius A. Burtea, Feb 18 2020
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 20 2008
EXTENSIONS
Extended by Emeric Deutsch, Jan 02 2009
a(79)-a(80) in b-file corrected by Georg Fischer, Feb 18 2020
STATUS
approved