A284812 - OEIS

A284812

Numbers n such that n' = d_1^1 + d_2^2 + ... + d_k^k where d_1, d_2, ..., d_k are the digits of n, with MSD(n) = d_1 and LSD(n) = d_k, and n' is the arithmetic derivative of n.

%I #14 Apr 10 2017 12:34:13

%S 4,34,78,47863,67277,472621,525038,5576423,7541551,12485411,13600033,

%T 41777431,48288701,64979641,97807441,136272511,153060223,201916441,

%U 214821521,225015223

%N Numbers n such that n' = d_1^1 + d_2^2 + ... + d_k^k where d_1, d_2, ..., d_k are the digits of n, with MSD(n) = d_1 and LSD(n) = d_k, and n' is the arithmetic derivative of n.

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

%p with(numtheory): P:=proc(q) local a,k,n,p; for n from 1 to q do a:=convert(n,base,10);

%p if add(a[k]^(nops(a)-k+1),k=1..nops(a))=n*add(op(2,p)/op(1,p),p=ifactors(n)[2])

%p then print(n); fi; od; end: P(10^9);

%Y Cf. A003415, A284213.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Apr 07 2017