A152990 Sum of proper divisors minus the number of proper divisors of Fibonacci number A000045(n).

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

Author

Omar E. Pol, Dec 20 2008

Keywords

• nonn

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.

Examples

			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
		

Links

• Georg Fischer, Table of n, a(n) for n = 1..80 [first 78 terms from B. D. Swan]

Crossrefs

Cf. A000005, A000045, A000203, A001065, A002808, A008578, A032741, A152770.

Programs

Magma

[DivisorSigma(1,f)-f-DivisorSigma(0,f)+1 where f is Fibonacci(n):n in [1..43] ]; // Marius A. Burtea, Feb 18 2020

Maple

with(combinat): with(numtheory): seq(sigma(fibonacci(n))-fibonacci(n)-tau(fibonacci(n))+1, n = 1 .. 45); # Emeric Deutsch, Jan 02 2009

Formula

a(n) = A000203(A000045(n)) - A000005(A000045(n)) - n + 1 = A001065(A000045(n)) - A032741(A000045(n)) = A152770(A000045(n)).

Extensions

Extended by Emeric Deutsch, Jan 02 2009

a(79)-a(80) in b-file corrected by Georg Fischer, Feb 18 2020