A108780 Numbers n such that (n / sum of digits of n) is a golden semiprime.

54, 135, 1122, 1386, 2244, 2805, 3366, 3927, 4488, 5301, 12369, 15318, 20445, 22977, 24534, 28623, 44979, 58941, 74169, 78588, 98892, 131454, 153363, 175272, 197181, 210693, 213206, 222132, 240792, 240999, 270891, 274122, 304580, 335038, 350267

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..2595 (terms below 10^11)

Example

1122 is a term because 1122/6=187 and 187=11*17 and 11*phi-17 = 0.798373... < 1.

Mathematica

goldQ[n_] := Module[{f = FactorInteger[n]}, If[Length[f] != 2, False, If[Max[f[[;; , 2]]] != 1, False, Abs[f[[2, 1]] - f[[1, 1]] * GoldenRatio] < 1]]]; sumDigits[n_] := Plus @@ IntegerDigits[n]; seqQ[n_] := Divisible[n, (sd = sumDigits[n])] && goldQ[n/sd]; Select[Range[360000], seqQ] (* Amiram Eldar, Nov 29 2019 *)

Crossrefs

Cf. A001101, A108540.

Sequence in context: A184067 A044305 A044686 * A057396 A286836 A304172

Adjacent sequences: A108777 A108778 A108779 * A108781 A108782 A108783

Keyword

base,nonn

Author

Jason Earls, Jun 26 2005

Status

approved