A381581 Numbers divisible by the sum of the digits in their Chung-Graham representation (A381579).

1, 2, 3, 4, 6, 8, 12, 16, 20, 21, 22, 24, 27, 28, 30, 40, 42, 44, 45, 48, 55, 56, 57, 58, 60, 66, 70, 72, 75, 76, 80, 84, 90, 92, 95, 96, 100, 102, 110, 111, 112, 115, 116, 120, 132, 135, 138, 140, 144, 150, 152, 153, 156, 168, 170, 175, 176, 180, 186, 190, 195, 198

Offset: 1

Author

Amiram Eldar, Feb 28 2025

Keywords

• nonn
• easy
• base

Comments

Numbers k such that A291711(k) divides k.

Analogous to Niven numbers (A005349) with the Chung-Graham representation (A381579) instead of the decimal representation.

A001906(k) = Fibonacci(2*k) is a term for all k >= 1.

If k is not divisible by 3 (A001651), then Fibonacci(2*k) + 1 is a term.

Examples

			4 is a term since A291711(4) = 1 divides 4.
6 is a term since A291711(6) = 2 divides 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A001651, A001906, A291711.

Subsequences: A381582, A381583, A381584, A381585.

Similar sequences: A005349, A049445, A064150, A328208, A328212.

Programs

Mathematica

f[n_] := f[n] = Fibonacci[2*n]; q[n_] := Module[{s = 0, m = n, k}, While[m > 0, k = 1; While[m > f[k], k++]; If[m < f[k], k--]; If[m >= 2*f[k], s += 2; m -= 2*f[k], s++; m -= f[k]]]; Divisible[n, s]]; Select[Range[200], q]

PARI

mx = 20; fvec = vector(mx, i, fibonacci(2*i)); f(n) = if(n <= mx, fvec[n], fibonacci(2*n));
isok(n) = {my(s = 0, m = n, k); while(m > 0, k = 1; while(m > f(k), k++); if(m < f(k), k--); if(m >= 2*f(k), s += 2; m -= 2*f(k), s++; m -= f(k))); !(n % s);}