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

Author

Jason Earls, Jun 26 2005

Keywords

• base
• nonn

Examples

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

Links

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

Crossrefs

Cf. A001101, A108540.

Programs

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 *)