A284813 Numbers m such that m' = d_1^k + d_2^(k-1) + ... + d_k^1 where d_1, d_2, ..., d_k are the digits of m, with MSD(m) = d_1 and LSD(m) = d_k, and m' is the arithmetic derivative of m.

0, 4, 766, 2587, 12629, 104977, 1068623, 1844423, 2056849, 2089207, 3126943, 3216923, 3410107, 11894353, 14467237, 20409227, 20544577, 23417957, 53531447, 57145091, 62206583, 114513821, 114691903, 124458617, 221281477, 230477407, 234265453, 246145657, 252609257, 311502431, 315969793, 320540147, 324465187

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..49

Example

766' = 385 = 7^3 + 6^2 + 6^1.

Maple

with(numtheory): P:=proc(q) local a, k, n, p; for n from 1 to q do a:=convert(n, base, 10);
if add(a[k]^k, k=1..nops(a))=n*add(op(2, p)/op(1, p), p=ifactors(n)[2])
then print(n); fi; od; end: P(10^9);

Prog

(Python)
from sympy import factorint
def ad(n): return 0 if n<2 else sum(n*e//p for p, e in factorint(n).items())
def ok(n): return ad(n) == sum(di**j for j, di in enumerate(map(int, str(n)[::-1]), 1))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 17 2025

Crossrefs

Cf. A003415, A284812

Sequence in context: A319943 A181200 A308141 * A306254 A068112 A007725

Adjacent sequences: A284810 A284811 A284812 * A284814 A284815 A284816

Keyword

nonn,base

Author

Paolo P. Lava, Apr 07 2017

Extensions

a(1) = 0 prepended by and a(21) onward from Michael S. Branicky, Oct 17 2025

Status

approved