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

1,2

Links

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

Example

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

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]

Prog

(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)); }

Crossrefs

Subsequence of A118363.

Subsequences: A000142, A377386.

Cf. A034968, A377384.

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

Sequence in context: A060765 A140110 A128397 * A120383 A324842 A055932

Adjacent sequences: A377379 A377380 A377384 * A377386 A377387 A377388

Keyword

nonn,easy,base

Author

Amiram Eldar, Oct 27 2024

Status

approved