A334308 Base phi Niven numbers: numbers divisible by the number of 1's in their base phi representation (A055778).

1, 2, 6, 12, 15, 16, 18, 20, 30, 35, 36, 45, 48, 55, 60, 70, 72, 78, 84, 90, 91, 95, 96, 98, 104, 108, 132, 144, 147, 154, 168, 175, 184, 189, 208, 224, 231, 232, 245, 252, 256, 261, 264, 270, 275, 280, 282, 287, 294, 315, 322, 324, 330, 336, 340, 342, 351, 357

Offset: 1

Author

Amiram Eldar, Apr 22 2020

Keywords

• nonn
• base

Examples

			6 is a term since its base phi representation is 1010.0001, and the number of 1's is 3, which is a divisor of 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• F. Michel Dekking, The sum of digits function of the base phi expansion of the natural numbers, arXiv:1911.10705 [math.NT], 2019.
• Ron Knott, Using Powers of Phi to represent Integers (Base Phi).
• Wikipedia, Golden ratio base.

Crossrefs

Cf. A005349, A049445, A055778, A064150, A064438, A064481, A118363, A328208, A328212, A333426.

Programs

Mathematica

phiDigSum[1] = 1; phiDigSum[n_] := Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[ Log[GoldenRatio, n]] ][[1]]; Select[Range[360], Divisible[#, phiDigSum[#]] &]