A377385 Factorial-base Niven numbers (A118363) k such that k/f(k) is also a factorial-base Niven number, where f(k) = A034968(k) is the sum of digits in the factorial-base representation of k.

1, 2, 4, 6, 8, 12, 16, 18, 24, 27, 36, 40, 48, 54, 72, 80, 96, 108, 120, 135, 144, 168, 175, 180, 192, 208, 210, 240, 280, 288, 336, 360, 384, 420, 432, 468, 480, 490, 572, 576, 594, 600, 630, 720, 732, 740, 750, 780, 784, 819, 840, 846, 861, 864, 888, 900, 924, 936, 945, 980, 984

Offset: 1

Author

Amiram Eldar, Oct 27 2024

Keywords

• nonn
• easy
• base

Examples

			8 is a term since 8/f(8) = 4 is an integer and also 4/f(4) = 2 is an integer.
		

Links

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

Crossrefs

Subsequence of A118363.

Subsequences: A000142, A377386.

Cf. A034968, A377384.

Analogous sequences: A376616 (binary), A377209 (Zeckendorf).

Programs

Mathematica

fdigsum[n_] := Module[{k = n, m = 2, r, s = 0}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, s += r; m++]; s]; q[k_] := Module[{f = fdigsum[k]}, Divisible[k, f] && Divisible[k/f, fdigsum[k/f]]]; Select[Range[1000], q]

PARI

fdigsum(n) = {my(k = n, m = 2, r, s = 0); while([k, r] = divrem(k, m); k != 0 || r != 0, s += r; m++); s;}
is(k) = {my(f = fdigsum(k)); !(k % f) && !((k/f) % fdigsum(k/f));}