A363462 - OEIS

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A363462

Numbers k for which the arithmetic derivative k' (A003415) is a Fibonacci number (A000045).

1, 2, 3, 5, 6, 7, 11, 13, 15, 17, 18, 19, 22, 23, 29, 31, 37, 38, 41, 43, 47, 53, 59, 61, 67, 71, 73, 75, 79, 83, 89, 93, 97, 101, 103, 106, 107, 109, 113, 127, 131, 137, 139, 145, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Any prime p (A000040) is a term because p' = 1 = A000045(1).

The union of A000040 and A362141.

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

1' = 0 = A000045(0), so 1 is a term.

6' = 5 = A000045(5), so 6 is a term.

22' = 13 = A000045(7), so 22 is a term.

MATHEMATICA

fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5 n^2 + {-4, 4}]; d[0] = d[1] = 0; d[n_] := n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[250], fibQ[d[#]] &] (* Amiram Eldar, Jul 05 2023 *)

PROG

(Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [p: p in [1..250]| IsSquare(5*u*u-4) or IsSquare(5*u*u+4) where u is Floor(f(p))];

CROSSREFS

Cf. A000040, A000045, A003415, A362141.

Sequence in context: A360007 A053329 A308420 * A260442 A359397 A098962

Adjacent sequences: A363459 A363460 A363461 * A363463 A363464 A363465

KEYWORD

nonn

AUTHOR

Marius A. Burtea, Jul 05 2023

STATUS

approved