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A293435 a(n) is the number of the proper divisors of n that are Fibonacci numbers (A000045). 9
0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 2, 3, 3, 1, 3, 1, 3, 2, 2, 1, 4, 2, 3, 2, 2, 1, 4, 1, 3, 2, 2, 2, 3, 1, 2, 3, 4, 1, 4, 1, 2, 3, 2, 1, 4, 1, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 3, 3, 3, 3, 1, 3, 2, 3, 1, 4, 1, 2, 3, 2, 1, 4, 1, 4, 2, 2, 1, 4, 2, 2, 2, 3, 1, 4, 2, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 4, 1, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10946

FORMULA

a(n) = Sum_{d|n, d<n} A010056(d).

a(n) = A005086(n) - A010056(n).

EXAMPLE

For n = 55, its proper divisors are [1, 5, 11], of which only two, namely 1 and 5 are in A000045, thus a(55) = 2.

MATHEMATICA

With[{s = Fibonacci@ Range[2, 40]}, Table[DivisorSum[n, 1 &, And[MemberQ[s, #], # != n] &], {n, 105}]] (* Michael De Vlieger, Oct 09 2017 *)

PROG

(PARI)

A010056(n) = { my(k=n^2); k+=(k+1)<<2; (issquare(k) || (n>0 && issquare(k-8))) }; \\ This function from Charles R Greathouse IV, Jul 30 2012

A293435(n) = sumdiv(n, d, (d<n)*A010056(d));

CROSSREFS

Cf. A000045, A005086, A010056, A293436.

Cf. also A293433.

Sequence in context: A101312 A241273 A154263 * A294901 A305818 A303757

Adjacent sequences:  A293432 A293433 A293434 * A293436 A293437 A293438

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 09 2017

STATUS

approved

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Last modified July 18 15:44 EDT 2019. Contains 325144 sequences. (Running on oeis4.)