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

1,2

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.

Links

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

Example

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

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]

Prog

(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); }

Crossrefs

Cf. A000045, A001651, A001906, A291711.

Subsequences: A381582, A381583, A381584, A381585.

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

Sequence in context: A084094 A217689 A018718 * A079647 A261205 A036451

Adjacent sequences: A381577 A381579 A381580 * A381582 A381583 A381584

Keyword

nonn,easy,base,new

Author

Amiram Eldar, Feb 28 2025

Status

approved