A240511 - OEIS

%I #54 Jan 11 2017 03:18:01

%S 1,2,3,4,5,6,7,8,9,90,336,4538775,183670618662,429548754570,

%T 3508325641459,3632460407839,9964270889420,10256010588126,

%U 509608423720931,589543349257828,75363159369591953,108765782844884700,360449417601592380,1574414276673927523

%N Numbers that are equal to the sum of their digits raised to each power from 1 to the number of digits.

%C Numbers with only 0 and 1 as digits are not considered. - _Paolo P. Lava_, Jan 11 2017

%H Giovanni Resta, <a href="/A240511/b240511.txt">Table of n, a(n) for n = 1..54</a> (terms < 10^32)

%H José de Jesús Camacho Medina, <a href="http://matematicofresnillense.blogspot.mx//2014/04/numeros-fresnillenses.html">Misterio de Números</a>

%F f(n) = Sum_{i,1,floor(log_10(n))+1} (Sum_{k,0,floor(log_10(n))+1} (floor(n/10^k) - 10*floor(n/10^(k + 1)))^(i)). If f(n)-n=0 then n is a number of this category. - _José de Jesús Camacho Medina_, Apr 07 2014

%e 9 = (9^1).

%e 90 = (9^1 + 0^1) + (9^2 + 0^2).

%e 336 = (3^1 + 3^1 + 6^1) + (3^2 + 3^2 + 6^2) + (3^3 + 3^3 + 6^3).

%t Q = Table[Sum[(Sum[(Floor[f/10^n] - 10*Floor[f/10^(n + 1)])^(i), {n, 0, Floor[Log[10, f]] + 1}]), {i, 1, Floor[Log[10, f]] + 1}], {f, 336}] - Range[336]; Flatten@ Position[Q, 0]

%t Select[Range[10^3], Plus @@ Power @@@ Tuples[{IntegerDigits @ #, Range@ IntegerLength@ #}] == # &] (* _Giovanni Resta_, Apr 30 2014 *)

%o (PARI) isok(n) = (d = digits(n)) && (n == sum(i=1, #d, sum(j=1, #d, d[j]^i))); \\ _Michel Marcus_, Apr 07 2014

%K nonn,base,fini

%O 1,2

%A _José de Jesús Camacho Medina_, Apr 06 2014

%E a(12)-a(24) from _Giovanni Resta_, Apr 07 2014