A284812 Numbers m such that m' = d_1^1 + d_2^2 + ... + d_k^k 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, 34, 78, 47863, 67277, 472621, 525038, 5576423, 7541551, 12485411, 13600033, 41777431, 48288701, 64979641, 97807441, 136272511, 153060223, 201916441, 214821521, 225015223, 332447113, 487155233, 494061433, 676545241, 721875103, 770493211, 1071601033, 1146560113

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..35

Example

47863' = 2104 = 4^1 + 7^2 + 8^3 + 6^4 + 3^5.

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]^(nops(a)-k+1), 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**i for i, di in enumerate(map(int, str(n)), 1))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 17 2025

Crossrefs

Cf. A003415, A284813.

Sequence in context: A227397 A365537 A281827 * A053902 A054464 A002101

Adjacent sequences: A284809 A284810 A284811 * A284813 A284814 A284815

Keyword

nonn,base

Author

Paolo P. Lava, Apr 07 2017

Extensions

a(1) = 0 prepended by and a(22)-a(29) from Michael S. Branicky, Oct 18 2025

Status

approved