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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. 3
125, 142, 1005, 118678, 706862, 18481615, 122003411, 30330043, 5923078409, 22110133333, 120175787632, 5971473681952 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..13.

EXAMPLE

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.

MAPLE

with(numtheory): for n from 2 to 7 do: i:=0:for k from 1 to 10^8 while(i=0) do:V:=convert(k, base, 10): n1:=nops(V):x:=divisors(k):n2:=nops(x):s:=sum(V[m]^n, m=1..n1):s1:=sum(x[a], a=1..n2):s1:=s1-1-k:if s=s1 then i:=1:printf ( "%d %d \n", n, k):else fi:od:od:

MATHEMATICA

(*** We suggest to change the value of x by successively x = 2, 3, ... and to keep the first term ***) Q[n_] := Module[{a = Total[Rest[Most[Divisors[n]]]]}, a == Total[IntegerDigits[n]^x]]; Select[Range[2, 5*10^7], Q]

PROG

(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

CROSSREFS

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

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

Sequence in context: A046759 A115938 A126895 * A069656 A196943 A307386

Adjacent sequences:  A202237 A202238 A202239 * A202241 A202242 A202243

KEYWORD

nonn,hard,base,more

AUTHOR

Michel Lagneau, Dec 16 2011

EXTENSIONS

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

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

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)