A270540 Numbers that are equal to the number of their digits multiplied by the sum of the fifth powers of the digits.

0, 1, 1232, 4100, 268542

Offset: 1

Author

José de Jesús Camacho Medina, Mar 18 2016

Keywords

• nonn
• base
• fini
• full

Comments

Terms up to 10^8.

No further terms after 10^7 since 10^k > k^2*9^5 beyond that point. - Ray Chandler, Apr 01 2016

Examples

			4100 is a term because 4100 = 4*(4^5+1^5+0^5+0^5).
		

Crossrefs

Cf. A055014.

Programs

Mathematica

Position[ Table[ IntegerLength[ k] Sum[( Floor[k/10^n] - 10 Floor[k/10^(n + 1)])^5, {n, 0, IntegerLength@ k}] - k, {k, 1, 10^6}], 0] // Flatten = {1, 1232, 4100, 268542}
Select[Range[10^7],With[{id=IntegerDigits[#]},#==Length[id]*Plus@@(id^5)]&] (* Ray Chandler, Apr 01 2016 *)

PARI

isok(n) = my(d=digits(n)); n == #d*sum(k=1, #d, d[k]^5); \\ Michel Marcus, Mar 25 2016

Extensions

a(5) from Michel Marcus, Mar 25 2016