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

1,6

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

Crossrefs

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

Sequence in context: A145831 A324482 A216406 * A177900 A214202 A019249

Adjacent sequences: A152987 A152988 A152989 * A152991 A152992 A152993

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