A202240 a(n) is the smallest number k such that the sum of the n-th powers of the digits of k equals the sum of the divisors of k other than 1 and k.

125, 142, 1005, 118678, 706862, 18481615, 122003411, 30330043, 5923078409, 22110133333, 120175787632, 5971473681952

Offset: 2

Author

Michel Lagneau, Dec 16 2011

Keywords

• nonn
• hard
• base
• more

Examples

			a(5) = 118678 because 1^5 + 1^5 + 8^5 + 6^5 + 7^5 + 8^5  = 90121, and sum of the divisors 1 < d < a(5) = sigma(118678) - 118678 - 1 = 90121.
		

Crossrefs

Cf. A070308 (n=2, "Canada perfect numbers").

Cf. A202279 (n=3), A202147 (n=4), A202285 (n=5).

Programs

PARI

f(k, n) = my(d=digits(k)); sum(i=1, #d, d[i]^n);
a(n) = my(k=1); while(f(k, n) != sigma(k)-k-1, k++); k; \\ Michel Marcus, Sep 29 2018

Extensions

a(8)-a(9) added by Amiram Eldar, Sep 29 2018

a(10)-a(13) from Giovanni Resta, Oct 04 2018